The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.
We have performed a large scale Monte Carlo simulation of a dilute classical Heisenberg model with ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions. We found that the model reproduces a reentrant spin-glass transition. That is, as the temperature is decreased, the magnetization increases rapidly below a certain temperature, reaches a maximum value, then ceases at some lower temperature. The low temperature phase was suggested to be a spin-glass phase that is characterized by ferromagnetic clusters.
uch experimental and theoretical efforts have been devoted in the past twenty years to search for a genuine thermodynamic reentrant phase transition from a ferromagnetic to either a paramagnetic or spin glass phase in disordered ferromagnets. So far, no real system or theoretical model of a short-range spin glass system has been shown to convincingly display such a reentrant transition. We present here results from Migdal-Kadanoff real-space renormalization-group calculations that provide for the first time strong evidence for ferromagnetic to paramagnetic reentrance in Potts spin glasses on h…
Spin excitations of single crystal Fe0.7Al0.3 were investigated over a wide range in energy and reciprocal space with inelastic neutron scattering. In the ferromagnetic phase, propagating spin wave modes become paramagnon-like diffusive modes beyond a critical wave vector q0, indicating substantial disorder in the long-range ordered state. In the spin glass phase, spin dynamics is strongly q-dependent, suggesting remnant short-range spin correlations. Quantitative model for S(energy,q) in the ``ferromagnetic'' phase is determined.
Magnetic behaviour of a mixed spin-1/2 and spin-1 Ising model on the diced lattice is studied by the use of an exact star-triangle mapping transformation. It is found that the uniaxial as well as biaxial single-ion anisotropy acting on the spin-1 sites may potentially cause a reentrant transition with two consecutive critical points. Contrary to this, the effect of next-nearest-neighbour interaction between the spin-1/2 sites possibly leads to a reentrant transition with three critical temperatures in addition to the one with two critical points only. The shape of the total magnetization versu…
We have performed an extensive muon spin relaxation study of the well known (Fe$_{1-x}$Mn$_{x}$)$_{75}$P$_{16}$B$_6$Al$_3$ reentrant spin glass. We find a strong increase of the dynamic as well as static muon depolarization rate at the paramagnetic to ferromagnetic transition temperature, $T_c$, and at $T_f$ ($T_f<T_c$) that corresponds to the onset of strong bulk magnetic irreversabilities. We find no critical dynamic signature of a freezing of the transverse $XY$ spin components at an intermediate temperature $T_{xy}$ ($T_f < T_{xy} < T_c$) where extra static order not contributing to the ma…
The extraordinary Hall effect coefficients $R_s(T)$ of the canonical spin glass alloys ${\bf Au}Fe 8 at%$ and ${\bf Au}Mn 8 at%$ and of an archetype reentrant system ${\bf Au}Fe 18 at%$ were measured as functions of temperature. The data show a critical cusp-like term superimposed on a smooth background for the spin glasses, and change of sign with temperature for the reentrant. The results can be interpreted consistently by invoking a chiral Hall effect contribution as proposed by Kawamura.
Magnetic-glass is a recently identified phenomenon in various classes of magnetic systems undergoing a first order magnetic phase transition. We shall highlight here a few experimentally determined characteristics of magnetic-glass and the relevant set of experiments, which will enable to distinguish a magnetic-glass unequivocally from the well known phenomena of spin-glass and reentrant spin-glass.
Performing light scattering experiments we show that introducing short-ranged attraction to a colloidal suspension of nearly hard spheres by addition of free polymer produces new glass transition phenomena. We observe a dramatic acceleration of the density fluctuations amounting to the melting of a colloidal glass. Increasing the strength of the attractions the system freezes into another nonergodic state sharing some qualitative features with gel states occurring at lower colloid packing fractions. This reentrant glass transition is in qualitative agreement with recent theoretical predictions…
Aging dynamics of a reentrant ferromagnet stage-2 Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied using DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and $T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a function of temperature $T$ shows a local maximum around 5.5 K, reflecting a frustrated nature of the ferromagnetic phase. It drastically increases with decreasing temperature below …
We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ and uniformly distributed random transverse fields ($Γ_0 \le Γ_i \le 2Γ_0$) in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (DMRG, combinatorial optimisation and strong disorder RG methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line ($h=0,Γ_0=1$) there is an infinite disorder quantum fixed point, while at the other end ($h=2,Γ_0=0$) there is a classical rando…
Stage-2 Cu$_{0.93}$Co$_{0.07}$Cl$_{2}$ graphite intercalation compound magnetically behaves like a reentrant ferromagnet near the multicritical point ($c_{MCP} \approx 0.96$). It undergoes two magnetic phase transitions at $T_{RSG}$ ($= 6.64 \pm 0.05$ K) and $T_{c}$ ($= 8.62 \pm 0.05$ K). The static and dynamic nature of the ferromagnetic and reentrant spin glass phase has been studied using DC and AC magnetic susceptibility. Characteristic memory phenomena of the DC susceptibility are observed at $T_{RSG}$ and $T_{c}$. The nonlinear AC susceptibility $χ_{3}^{\prime}$ has a positive local maxi…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
A mean-field multi-spin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense, D is infinite, in the paramagnetic phase and on its boundary the mapping is exact. In this limit the method provides a general and simple rule to obtain exactly the upper phase boundaries. We provide even simple effective rules to find crossover surfaces and correlation functions. We apply the mapping to several spin glass models.
The field-cooled magnetization (FCM) processes of Ising spin glasses under relatively small fields are investigated by experiment on Fe_{0.55}Mn_{0.45}TiO_3 and by numerical simulation on the three-dimensional Edwards-Anderson model. Both results are explained in a unified manner by means of the droplet picture. In particular, the cusp-like behavior of the FCM is interpreted as evidence, not for an equilibrium phase transition under a finite magnetic field, but for a dynamical (`blocking') transition frequently observed in glassy systems.
We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents $η$ and $z$ vary with the form of the interaction distribution, indicating non-universality at Ising spin glass transitions. These results confirm conclusions drawn from numerical data for dimension 3.
We consider the random field Ising model and show rigorously that the spin glass susceptibility at equilibrium is always bounded by the ferromagnetic susceptibility, and therefore that no spin glass phase can be present at equilibrium out of the ferromagnet critical line. When the magnetization is, however, fixed to values smaller than the equilibrium one, a glassy phase can exist, as we show explicitly on the Bethe lattice.
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 investigate the distributions of the link overlap, P(Q), in 3-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states, and calculate its contribution to P(Q). We find that the distribution over this set does not become trivial as the system size increases.
We argue that the chaotic temperature effect predicted in Ising spin glasses should be stronger when one considers continuous (XY, Heisenberg) kind of spins, due to bigger entropic fluctuations. We then discuss the behavior of 3d spin glasses using the Migdal-Kadanoff Renormalization Group for Ising and XY spins, where we show explicitly that the chaotic length scale, the length beyond which equilibrium configurations are completly reshuffled when one changes temperature, could be far smaller for XY than for Ising spins. These results could thus explain why experiments are seeing a stronger re…
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lat…
The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Calro (MC) method on one hand, and the equilibrium magnetization of the same system is evaluated by the exchang MC method on the other hand. The two types of simulation reveal intriguing glassy (nonequilibrium) dynamic properties of the FC magnetization (FCM) of the system. Particularly, the FCM decrease is observed when the FC process is halted at a low temperater, although its value is smaller than the corresponding equilibrium value. We present a comprehensive interpretation of such peculiar pheno…
Nearest-neighbor-interaction Ising spin glasses are studied on three different hierarchical lattices, all of them belonging to the Wheatstone-Bridge family. It is shown that the spin-glass lower critical dimension in these lattices should be greater than 2.32. Finite-temperature spin-glass phases are found for a lattice of fractal dimension $D \approx 3.58$ (whose unit cell is obtained from a simple construction of a part of the cubic lattice), as well as for a lattice of fractal dimension close to five.
We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job at describing the spatial shape of the correlation function of the out-equilibrium Edwards-Anderson Ising model in two dimensions.
The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.
Identities and inequalities are proved for the order parameters, correlation functions and their derivatives of the Ising spin glass. The results serve as additional evidence that the ferromagnetic phase is composed of two regions, one with strong ferromagnetic ordering and the other with the effects of disorder dominant. The Nishimori line marks a crossover between these two regions.
We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p δ(J - 1) + (1-p) δ(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly re…
We analyze the limits inherent to the inverse reconstruction of a pairwise Ising spin glass based on susceptibility propagation. We establish the conditions under which the susceptibility propagation algorithm is able to reconstruct the characteristics of the network given first- and second-order local observables, evaluate eventual errors due to various types of noise in the originally observed data, and discuss the scaling of the problem with the number of degrees of freedom.
Equilibrium numerical data on the three dimensional bimodal interaction Ising spin glass up to size L=48 show that corrections to scaling, which are known to be strong, behave in a non-monotonic manner with size. Extrapolation to the infinite size thermodynamic limit is difficult; however the large L data indicate that the ordering temperature Tc lies significantly higher than the values which have been estimated from previous numerical work limited to smaller sizes. In view of the present results it is at the least premature to conclude that the three dimensional bimodal and Gaussian Ising sp…
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately established using a standard criterion, critical exponents and correction terms can be readily estimated by extrapolating measurements made in the thermodynamic limit regime. The data show that the critical exponents of the susceptibility $γ$ and of the correlation length $ν$ depend on the form of the interaction distribution. This observation implies that quite gener…
The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar, Anderson and Stein have been re-examined and a new fixed point has been found. The fixed points which have previously been studied are found to be inappropriate. It is shown that the renormalization group equations themselves directly imply that the spin glass phase is replica symmetric, in agreement with droplet model expectations, when the range exponent $σ$ l…
By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.
By combining the scaling relation of Amoruso {\it et al.}, PRL {\bf 97}, 267202 (2006) with standard droplet model assumptions, a value $θ= (\sqrt{6} - 3) / 2$ is obtained. This conjecture is reasonably consistent with the best existing numerical calculations, and may be exact.
The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control parameter is tuned. Due to its microscopic properties the model is straightforwardly extendable to finite dimensions in any geometry.
We compute and analyze couples of ground states of 3D spin glasses before and after applying a volume perturbation which adds to the Hamiltonian a repulsion from the true ground state. The physical picture based on Replica Symmetry Breaking is in excellent agreement with the observed behavior.
A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a self-consistent integral equation. By solving the self-consistency condition numerically, we find that there are two temperature scales characterizing the glass transition. At the first, higher temperature, the glass order parameter becomes non-vanishing, and at the second, freezing temperature, it saturates to its maximal value. The effect of magnetic field and the exi…
We show that the dynamical behavior of the 3D Ising spin glass with Gaussian couplings is not compatible with a droplet dynamics. We show that this is implied from the data of reference cond-mat/9904143, that, when analyzed in an accurate way, give multiple evidences of this fact. Our study is based on the analysis of the overlap-overlap correlation function, at different values of the separation r and of the time t.
We study the correlation length of the two-dimensional Edwards-Anderson Ising spin glass with bimodal interactions using a combination of parallel tempering Monte Carlo and a rejection-free cluster algorithm in order to speed up equilibration. Our results show that the correlation length grows ~ exp(2J/T) suggesting through hyperscaling that the degenerate ground state is separated from the first excited state by an energy gap ~4J, as would naively be expected.
We study temperature chaos in a two-dimensional Ising spin glass with random quenched bimodal couplings, by an exact computation of the partition functions on large systems. We study two temperature correlators from the total free energy and from the domain wall free energy: in the second case we detect a chaotic behavior. We determine and discuss the chaos exponent and the fractal dimension of the domain walls.
The emergence of glassy behavior of the random field Ising model (RFIM) is investigated using an extended mean-field theory approach. Using this formulation, systematic corrections to the standard Bragg-Williams theory can be incorporated, leading to the appearance of a glassy phase, in agreement with the results of the self-consistent screening theory of Mezard and Young. Our approach makes it also possible to obtain information about the low temperature behavior of this glassy phase. We present results showing that within our mean-field framework, the hysteresis and avalanche behavior of the…
We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior can not be completely excluded.
We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory. Similar results are also obtained in two dimensions.
We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relati…
Using Monte Carlo simulations, we have studied the relaxation of energy of the three-dimensional Ising spin-glass model in aging process. Our finite-size-scaling analysis on the isothermal energy decay after the quench suggests strongly that the energy relaxes by coarsening of domain walls in agreement with the droplet theory. We have also evaluated relaxation times required for spin configurations in small systems, which are regarded as isolated droplets, to flip globally. The results support the fundamental assumption of the droplet theory that coarsening of domain walls, in case of spin gla…
The Griffiths inequalities for Ising spin glasses are proved on the Nishimori line with various bond randomness which includes Gaussian and $\pm J$ bond randomness. The proof for Ising systems with Gaussian bond randomness has already been carried out by Morita et al, which uses not only the gauge theory but also the properties of the Gaussian distribution, so that it cannot be directly applied to the systems with other bond randomness. The present proof essentially uses only the gauge theory, so that it does not depend on the detail properties of the probability distribution of random interac…
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.
Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.
The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-gla…
Linear and nonlinear dynamic properties of a reentrant ferromagnet Cu$_{0.2}$Co$_{0.8}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound are studied using AC and DC magnetic susceptibility. This compound undergoes successive phase transitions at the transition temperatures $T_{h}$ (= 16 K), $T_{c}$ (= 9.7 K), and $T_{RSG}$ (= 3.5 K). The static and dynamic behaviors of the reentrant spin glass phase below $T_{RSG}$ are characterized by those of normal spin glass phase with critical exponent $β$ = 0.57 $\pm$ 0.10, a dynamic critical exponent $x$ = 8.5 $\pm$ 1.8, and an exponent $p$ (= 1.55…
Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic properties of the model, and of probabilistic properties of a pair correlator, which is a fluctuating object in disordered systems. PACS numbers: 02.50.-r, 05.20.-y, 05.70.Fh, 64.60.ae, 75.10.-b, 75.10.Hk, 87.10.+e Keywords: statistical physics, magnetism, spin glass, neural networks
Numerical data on scaling of the normalized Binder cumulant and the normalized correlation length are shown for the Thermodynamic limit regime, first for canonical Ising ferromagnet models and then for a range of Ising spin glass models. A fundamental Renormalization Group Theory rule linking the critical exponents for the two observables is well obeyed in the Ising models, but not for the Ising spin glasses in dimensions three and four. We conclude that there is a violation of a standard Josephson hyperscaling rule in Ising spin glasses.
We study the four-dimensional Ising spin glass with Gaussian and bond-diluted bimodal distributed interactions via large-scale Monte Carlo simulations and show via an extensive finite-size scaling analysis that four-dimensional Ising spin glasses obey universality.
We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional spin glasses obey universality.
Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a \emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature pha…
We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard interaction, by noticing that their Hamiltonian is a function of the number operator only. The thermodynamical properties are mapped to the classical Ghatak-Sherrington spin-glass model while the the Density of States (DoS) is related to its joint spin-field distribution. We discuss the presence of the pseudogap in the DoS with the help of this mapping.
The time and temperature dependence of the field-cooled magnetization of a three dimensional Ising spin glass, Fe_{0.5}Mn_{0.5}TiO_{3}, has been investigated. The temperature and cooling rate dependence is found to exhibit memory phenomena that can be related to the memory behavior of the low frequency ac-susceptibility. The results add some further understanding on how to model the three dimensional Ising spin glass in real space.
We consider the thermodynamics of an infinite-range Ising p-spin glass model with an additional r-spin ferromagnetic interaction. For r=2 there is a continuous transition to a ferromagnetic phase, while for r>2 the transition is first order. We find both glassy and non-glassy ferromagnetic phases, with replica symmetry breaking of both the one step and full varieties. We obtain new results for the case where r=p>2, demonstrating the existence of a non-glassy ferromagnetic phase, of significance to error-correcting codes.
