Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L^3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x < 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature T_sg proportional to x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behaviour found for the Sherrington-Kirkpatrick model.
We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free energy per site, in analogy with the results of Aizenman, Sims and Starr for non-diluted models. We also prove some stability properties of the optimal RMOSt, analogous to the one found by Guerra for non-diluted models.
By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and syst…
We present a method derived by cavity arguments to compute the spin-glass and higher-order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated to the existence of a non-zero solution of a homogeneous linear integral equation. Higher order susceptibilities, relevant for critical dynamics through the parameter exponent $λ$, can be expressed at criticality as integrals involving the critical eigenvector. The numerical evaluation of the corresponding analytic expressions is discussed. The method is illustrated in the context of th…
We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a short-range model. We are therefore able to study both the mean-field and non-mean-field regimes. For one value of sigma, in the non-mean-field regime, we find evidence that the chiral glass transition temperature may be somewhat higher than the spin glass transition temperature. For the other values of sigma we see no evidence for this.
Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of much interest for over the past fifteen years. Their low temperature strongly correlated state can be mapped onto the proton disordered state of common water ice and, consequently, spin ices display the same low temperature residual Pauling entropy as water ice. Interestingly, it was found in a previous study [X. Ke {\it et. al.} Phys. Rev. Lett. {\bf 99}, 137203 (2007)] that, upon dilution of the magnetic rare-earth ions (Dy^{3+} and Ho^{3+}) by non-magnetic Yttrium (Y^{3+}) ions, the residual entropy depends {\it non…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating the model is drastically reduced with respect to the fully connected version and larger sizes can be studied. We fin…
We study link-diluted $\pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.
We study the temperature-dilution phase diagram of a site-diluted Heisenberg antiferromagnet on a fcc lattice, with and without the Dzyaloshinskii-Moriya anisotropic term, fixed to realistic microscopic parameters for $IIB_{1-x} Mn_x Te$ (IIB=Cd, Hg, Zn). We show that the dipolar Dzyaloshinskii-Moriya anisotropy induces a finite-temperature phase transition to a spin glass phase, at dilutions larger than 80%. The resulting probability distribution of the order parameter P(q) is similar to the one found in the cubic lattice Edwards-Anderson Ising model. The critical exponents undergo large fini…
We revisited, by means of numerical simulations, the one dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean field theories. In these models the probability that two spins at distance $r$ interact (via a disordered interactions, $J_{ij}=\pm 1$) decays as $r^{-ρ}$. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for $ρ=5/3$ and $ρ=9/5$. We have obtained strong evidence for divergences of the previous observables at a non zero critical temperature. We discuss the behavior of the criti…
By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L^3 sites of a simple cubic lattice, and point along a given crystalline axis. For x_c< x<=1, where x_c = 0.65, we find an antiferromagnetic phase below a temperature which vanishes as x tends to x_c from above. At lower values of x, we find an equilibrium spin-glass (SG) phase below a temperature given by k_B T_{sg} = x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy. We study (a) the relative mean square deviation D_q^2 of …
We investigate a possible relation between frustration and phase-transition points in spin glasses. The relation is represented as a condition of the number of frustrated plaquettes in the lattice at phase-transition points at zero temperature and was reported to provide very close points to the phase-transition points for several lattices. Although there has been no proof of the relation, the good correspondence in several lattices suggests the validity of the relation and some important role of frustration in the phase transitions. To examine the relation further, we present a natural extens…
A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Using different finite size scaling methods evidence for a spin-glass transition is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new…
We have investigated a phase transition of a long-range RKKY Ising spin glass \dyyrusi by means of the dc and the ac magnetization measurements. The static nonlinear susceptibility $χ_{2}$ exhibits a divergent behavior toward $\Tg$ $=$ 1.925 K with the exponent of $γ$ $=$ 1.08. The characteristic relaxation time $τ$ obtained from the ac magnetization measurements also diverges to the same $\Tg$ with the exponent of $zν$ $=$ 1.9 in zero static field . These results indicate the spin glass phase transition belonging to the mean-field universality class, in which the exponents of $\gammaMF$ and $…
Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and rando…
Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that bond-dilution enables the numerical treatment of larger lattices, and that the subsequent combination of such data at various bond densities into a finite-size scaling Ansatz produces more robust scaling behavior. In the present study we test the potential of such a procedure, in particular, to obtain the stiffness exponent for the hierarchical Migdal-Kadanoff l…
The spin-glass phase in the $\LHx$ compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J=8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.
We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper, we use the parallel tempering algorithm to study the thermodynamics for different diluted ratio x and give the phase diagram. The presence of both frustration and disorder results in a spin-glass phase, which exists between the stripe antiferromagnetic phase and the Neel phase. We present the ground-state energy of T -> 0 and the size-dependence of Edwards-…
In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a complete control of the system, proving annealing for the infinite volume free energy, and a central limit theorem for the suitably rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy fluctuations, on the scale 1/N, converge in the infinite volume limit to a non-Gaussian random variable, whose variance diverges at the boundary of th…
We derive the equilibrium phase diagram of the classical dipolar Ising antiferromagnet at the mean-field level on a geometry that mimics the two dimensional Kagome lattice. Our mean-field treatment is based on the combination of the cluster variational Bethe-Peierls formalism and the cavity method, developed in the context of the glass transition, and is complementary to the Monte Carlo simulations realized in [Phys. Rev. B 98, 144439 (2018)]. Our results confirm the nature of the low temperature crystalline phase which is reached through a weakly first-order phase transition. Moreover, they a…
The low temperature phase of discontinuous mean-field spin glasses is characterized by the appearance of an exponential number of metastable states. Which ones among these states dominate the out-of-equilibrium dynamics of these systems? In order to answer this question, we compare high-precision numerical simulations of a diluted $p$-spin model with a cavity computation of the threshold energy. Our main conclusion is that the aging dynamics is dominated by different layers of metastable states depending on the cooling schedule. In order to perform our analysis, we present a method for computi…
Puzzling anomalies previously observed in multipulse NMR experiments in natural abundance 29Si [A.E. Dementyev, D. Li, K. MacLean, and S.E. Barrett, Phys. Rev. B 68, 153302 (2003)] such as long-lived spin echoes and even-odd asymmetries, are also found in polycrystalline C60. Further experiments controlling the phases and tilting angles of the pulse trains, as well as analytical and numerical calculations allowed us to explain the origin of these anomalies. We prove that the observation of long magnetization tails requires two conditions: i) an rf field inhomogeneity able to produce different …
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for graphs with uniform connectivity. The resulting ground state energy is in perfect agreement with numerical simulations. For fluctuating connectivity graphs, the same Ansatz can be used in a variational way: For p-spin models (known as p-XOR-SAT in computer science) it provides the exact configurational entropy together with the dynamical and static critical conn…
The nonlinear magnetic $χ_{3}$ and spin-glass $χ_{sg}$ susceptibilities in zero applied field are obtained, from tempered Monte Carlo simulations, for three different spin glasses (SGs) of Ising spins with quenched site disorder. We find that the relation $-T^3χ_3=χ_{sg}-2/3$ ($T$ is the temperature), which holds for Edwards-Anderson SGs, is approximately fulfilled in canonical-like SGs. For nearest neighbor antiferromagnetic interactions, on a 0.4 fraction of all sites in fcc lattices, as well as for spatially disordered Ising dipolar (DID) systems, $-T^3χ_3$ and $χ_{sg}$ appear to diverge in…
We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of finite (average or regular) degree, the networks studied here are randomly bond-diluted to an overall density $p$, such that the average degree diverges as $\sim pN$ with the system size $N$. Ground-state energies are obtained with high accuracy for random instances over a wide range of fixed $p$. Since this is a NP-hard combinatorial problem, we employ the Ex…
In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an interpolation procedure that stresses the relation between interpolation methods and the cavity method. As a byproduct we obtain self-averaging identities that generalize the Ghirlanda-Guerra ones to the multi-overlap case.
We present analytical and numerical evidence for the validity of an effective S=1/2 approach to the description of random field generation in S>=1, and especially in an S=1, dipolar spin glass models with strong uniaxial Ising anisotropy and subject to weak external magnetic field Bx transverse to the Ising direction. Explicitely Bx-dependent random fields are shown to naturally emerge in the effective low-energy description of a microscopic S=1 toy model. We discuss our results in relation to recent theoretical studies pertaining to the topic of Bx-induced random fields in the LiHo$_x$Y$_{1-x…
The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming ac…
In a recent letter [Phys. Rev. Lett. {\bf 75}, 2360 (1996)] we briefly discussed the existence and nature of ferroelectric order in positionally disordered dipolar materials. Here we report further results and give a complete description of our work. Simulations of randomly frozen and dynamically disordered dipolar soft spheres are used to study ferroelectric ordering in non-crystalline systems. We also give a physical interpretation of the simulation results in terms of short- and long-range interactions. Cases where the dipole moment has 1, 2, and 3 components (Ising, XY and XYZ models, resp…
We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random…
We study partially occupied lattice systems of classical magnetic dipoles which point along randomly oriented axes. Only dipolar interactions are taken into account. The aim of the model is to mimic collective effects in disordered assemblies of magnetic nanoparticles. From tempered Monte Carlo simulations, we obtain the following equilibrium results. The zero temperature entropy approximately vanishes. Below a temperature T_c, given by k_B T_c= (0.95 +- 0.1)x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy and x is the site occupancy rate, we find a spin glass phase. In …
An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization le…
We study equilibration and ordering in the classical dipolar kagome Ising antiferromagnet, which we show behaves as a disorder-free fragile spin glass. By identifying an appropriate order parameter, we demonstrate a transition to the ordered state proposed by Chioar et al. [Phys. Rev. B 93, 214410 (2016)] with a 12-site unit cell that breaks time-reversal and sublattice symmetries, and further provide evidence that the nature of the transition is first order. Upon approaching the transition, the spin dynamics slow dramatically. The system readily falls out of equilibrium, overshooting the tran…
The physics of the spin glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. While most theoretical studies have focused on the Edwards-Anderson model of Ising spins with only discrete `up/down' directions, such Ising systems are experimentally rare. LiHo$_{x}$Y$_{1-x}$F$_{4}$, where the Ho$^{3+}$ moments are well described by Ising spins, is an almost ideal Ising SG material. In LiHo$_{x}$Y$_{1-x}$F$_{4}$, the Ho$^{3+}$ moments interact predominantly via the inherently frustrated magnetostatic dipole…
A method is presented for measuring the integrated response in Ising spin system without applying any perturbing field. Large-scale simulations are performed in order to show how the method works. Very precise measurements of the fluctuation-dissipation ratio are presented for 3 different Ising models: the 2-dimensional ferromagnetic model, the mean-field diluted 3-spin model, and the 3-dimensional Edwards-Anderson model.
Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both analytically and numerically because of long-ranged interactions between spins as well as rare region effects. We study a new type of anisotropic dilute dipolar Ising system in three dimensions [Phys. Rev. Lett. {\bf 114}, 247207 (2015)] that arises as an effective description of randomly diluted classical spin ice, a prototypical spin liquid in the disorder-free limit, with a small fraction $x$ of non-magnetic impurities. Metropolis algorithm within a parallel thermal tempering scheme fails to achieve equilibration …
We report measurements of the ac susceptibility of the cooperative paramagnet Tb2Ti2O7 in a strong magnetic field. Our data show the expected saturation maximum in chi(T) and also an unexpected low frequency dependence (< 1 Hz) of this peak, suggesting very slow spin relaxations are occurring. Measurements on samples diluted with nonmagnetic Y3+ or Lu3+ and complementary measurements on pure and diluted Dy2Ti2O7 strongly suggest that the relaxation is associated with dipolar spin correlations, representing unusual cooperative behavior in a paramagnetic system.
Heat bath Monte Carlo simulations have been used to study a 12-state discretized Heisenberg model with a new type of random field on simple cubic lattices of size $128 \times 128 \times 128$. The 12 states correspond to the [110] directions of a cube. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a random field which consists of adding an energy $h_R$ to two of the 12 spin states, chosen randomly and independently at each site. We report on the case $h_R / J = 3$, which has a sharp phase transition at about $T_c / J = 1.40625$. Below $T_c$, the model …
We simulate the dc magnetic response of the diluted dipolar-coupled Ising magnet LiHo\(_{0.045}\)Y\(_{0.955}\)F\(_4\) in a transverse field, using exact diagonalization of a two-spin Hamiltonian averaged over nearest-neighbour configurations. The pairwise model, incorporating hyperfine interactions, accounts for the observed drop-off in the longitudinal (c-axis) susceptibility with increasing transverse field; with the inclusion of a small tilt in the transverse field, it also accounts for the behavior of the off-diagonal magnetic susceptibility. The hyperfine interactions do not appear to lea…
We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and link density low enough), where spins are long range correlated, even if the ground states energy stiffness is null. In other words, in this region twisting the boundary conditions cost no energy, but spins are long range correlated by means of pure entropic effects.
The spin-glass transition in external magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Evidence for a spin-glass transition in magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field.
An analytical model of non-Gaussian energy landscape of low-temperature fluids is developed based on the thermodynamics of the fluid of dipolar hard spheres. The entire excitation profile of the liquid, from the high temperatures to the point of ideal-glass transition, has been obtained from the Monte Carlo simulations. The fluid of dipolar hard spheres loses stability when reaching the point of ideal-glass transition transforming via a first-order transition into a columnar liquid phase of dipolar chains locally arranged in a body-centered tetragonal order.
We study from tempered Monte Carlo simulations the magnetic phase diagram of a textured dipolar Ising model on a face centered cubic lattice. The Ising coupling of the model follow the dipole-dipole interaction. The Ising axes are distributed with a uniaxial symmetry along the $\hat{z}$ direction with a gaussian probability density of the polar angles. This distribution provides a quenched disorder realization of the dipolar Ising model making a continuous link between the parallel axes dipoles and the random axes dipole models. As expected the phase diagram presents three distinctive phases: …
At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $η\approx 0$ and $ν\approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the…
Dynamic nonlinear (cubic) susceptibility in quantum d-dimensional Ising spin glass with short-range interactions is investigated on the basis of quantum droplet model and quantum-mechanical nonlinear response theory. Nonlinear response depends on the tunneling rate for a droplet which regulates the strength of quantum fluctuations. It shows a strong dependence on the distribution of droplet free energies and on the droplet length scale average. Comparison with recent experiments on quantum spin glasses like disordered dipolar quantum Ising magnet is discussed.
We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator, omega=1.0(1). We also determine the critical exponents nu and eta. Taking into a…
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric (RS) approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitio…
The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy…
AC susceptibility measurements are presented on the dilute, dipolar coupled, Ising magnet LiHo$_x$Y$_{1-x}$F$_4$ for a concentration $x = 0.045$. The frequency and temperature dependences of the susceptibility show characteristic glassy relaxation. The absorption spectrum is found to broaden with decreasing temperature suggesting that the material is behaving as a spin glass and not as an exotic spin liquid as was previously observed. A dynamical scaling analysis suggests a spin glass transition temperature of 42.6 mK $\pm 2$ mK with an exponent $zν= 7.8 \pm 0.23$.
Dilute dipolar systems in three dimensions are expected to undergo a spin glass transition as the temperature decreases. Contrary to this, we find from Wang-Landau Monte Carlo simulations that at low concentrations $x$, dipoles randomly placed on a cubic lattice with dipolar interactions do not undergo a phase transition. We find that in the thermodynamic limit the ``glass'' transition temperature $T_g$ goes to zero as $1/\sqrt{N}$ where $N$ is the number of dipoles. The entropy per particle at low temperatures is larger for lower concentrations ($x=4.5%$) than for higher concentrations ($x=20…
Sun Yat-sen University（中山大学）；RIKEN Center for Brain Science（理化学研究所脑科学中心）
Deep learning has become a powerful and popular tool for a variety of machine learning tasks. However, it is challenging to understand the mechanism of deep learning from a theoretical perspective. In this work, we propose a random active path model to study collective properties of deep neural networks with binary synapses, under the removal perturbation of connections between layers. In the model, the path from input to output is randomly activated, and the corresponding input unit constrains the weights along the path into the form of a $p$-weight interaction glass model. A critical value o…
We consider an alternative to the usual spin glass paradigm for disordered magnetism, consisting of the previously unstudied combination of frustrated magnetic interactions and pseudo-dipolar disorder in spin positions. We argue that this model represents a general limiting case for real systems as well as a realistic model for certain binary fluorides and oxides. Furthermore, it is of great relevance to the highly topical subjects of the Coulomb phase and `charge ice'. We derive an analytical solution for the ground state phase diagram of a model system constructed in this paradigm and identi…
In LiHo_xY_{1-x}F4, the magnetic Holmium Ho^{3+} ions behave as effective Ising spins that can point parallel or antiparallel to the crystalline c-axis. The predominant inter-Holmium interaction is dipolar, while the Y^{3+} ions are non-magnetic. The application of a magnetic field Bx transverse to the c-axis Ising direction leads to quantum spin-flip fluctuations, making this material a rare physical realization of the celebrated transverse field Ising model. The problems of classical and transverse-field-induced quantum phase transitions in LiHo_xY_{1-x}F_4 in the dipolar ferromagnetic (x=1)…
We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(T) ~ x, in disagreement …
Aging in a two-dimensional Ising spin model with both ferromagnetic exchange and antiferromagnetic dipolar interactions is established and investigated via Monte Carlo simulations. The behaviour of the autocorrelation function $C(t,t_w)$ is analyzed for different values of the temperature, the waiting time $t_w$ and the quotient $δ=J_0/J_d$, $J_0$ and $J_d$ being the strength of exchange and dipolar interactions respectively. Different behaviours are encountered for $C(t,t_w)$ at low temperatures as $δ$ is varied. Our results show that, depending on the value of $δ$, the dynamics of this non-d…
By tempered Monte Carlo simulations, an Almeida-Thouless (AT) phase-boundary line in site-diluted Ising spin systems is searched for. Spins interact only through dipolar fields and occupy a small fraction of lattice sites. The spin-glass susceptibility of these systems and of the Sherrington-Kirkpatrick model are compared. The correlation length as a function of system size and temperature is also studied. The results obtained are contrary to the existence of an AT line.
Using molecular dynamics simulation, we study dipolar glass in crystals composed of slightly spheroidal, polar particles and spherical, apolar impurities between metal walls. We present physical pictures of ferroelectric glass, which have been observed in relaxors, mixed crystals (such as KCN$_x$KBr$_{1-x}$), and polymers. Our systems undergo a diffuse transition in a wide temperature range, where we visualize polar nanoregions (PNRs) surrounded by impurities. In our simulation, the impurities form clusters and their space distribution is heterogeneous. The polarization fluctuations are enhanc…
The behavior of many magnetic and dielectric solids, and the more contemporary magnetic super-lattices, is governed by dipolar interactions. They are anisotropic and long-ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterised by a plethora of relaxation times.These systems are well-captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions (J) and long-range dipolar interactions (D). Depending on the relative interaction strength Γ =J/D, there are four phases of distinct magnetic …
