Ordering properties of XY-like spin-glass magnets with an easy-plane magnetic anisotropy are studied based on a symmetry consideration and the results of recent numerical simulations on the pure Heisenberg and XY spin-glass models. The effects of an easy-plane-type uniaxial anisotropy, a random magnetic anisotropy and an applied magnetic field are investigated. In the XY regime in zero field, the "spin-chirality decoupling" persists even under the random magnetic anisotropy, escaping the "spin-chirality recoupling" phenomenon which inevitably occurs in the Heisenberg regime. Contrast between the scalar chiral order and the vector chiral order is emphasized. Implications to experiments are discussed.
Exploiting an approach due to Singh and Fisher I show that in the high dimension limit the ordering temperature of near neighbour Ising Spin Glasses drops linearly with the kurtosis of the interaction distribution, in excellent agreement with accurate high temperature series data of Daboul, Chang and Aharony. At lower dimensions the linear relation no longer applies strictly but the kurtosis can still be taken to be an appropriate parameter for ranking different systems. I also compare the series estimates with simulation and Migdal-Kadanoff estimates where these are available.
Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without randaom magnetic anisotropy by dynamical Monte Carlo simulations. In isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminisecnt of the one observed in the mean-field model. In anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.
For five different Heisenberg spin glass systems, torque experiments were performed in applied magnetic fields up to $4 T$. The Dzyaloshinski-Moriya random anisotropy strengths, the in-field torque onset temperatures, and the torque relaxation were measured. Critical exponents were estimated independently using a standard protocol. The data are strong evidence for a true spin glass ordered state which survives under high applied magnetic fields; they can be interpreted consistently in terms of a chiral ordering model with replica symmetry breaking as proposed by Kawamura and coworkers.
An overview is given of experimental data on Heisenberg Spin Glass materials so as to make detailed comparisons with numerical results on model Heisenberg spin glasses, with particular reference to the chiral driven ordering transition scenario due to Kawamura and collaborators. On weak anisotropy systems, experiments show critical exponents which are very similar to those estimated numerically for the model Heisenberg chiral ordering transition but which are quite different from those at Ising spin glass transitions. Again on weak anisotropy Heisenberg spin glasses, experimental torque data s…
Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real spin-glass transition and its experimental consequence on the ordering of Heisenberg-like spin glasses are discussed.
Glasses are featured with a disordered amorphous structure, being opposite to crystals that are constituted by periodic lattices. In this study we report that the exceptional thermodynamic and kinetic stability of an ultra-stable binary ZrCu metallic glass, fabricated by high-temperature physical vapor deposition, originates from ubiquitous crystal-like medium range order (MRO) constituted by Voronoi polyhedron ordering with well-defined local translational symmetry beyond nearest atomic neighbors. The crystal-like MRO significantly improves the thermodynamic and kinetic stability of the glass…
In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or ``observable'', states and (probably) unphysical, ``invisible'' states. We review replica symmetry breaking, and describe what it would mean in short-ranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot desc…
Aging in spin glasses (and in some other systems) reveals astonishing effects of `rejuvenation and memory' upon temperature changes. In this paper, we propose microscopic mechanisms (at the scale of spin-spin interactions) which can be at the origin of such phenomena. Firstly, we recall that, in a frustrated system, the effective average interaction between two spins may take different values (possibly with opposite signs) at different temperatures. We give simple examples of such situations, which we compute exactly. Such mechanisms can explain why new ordering processes (rejuvenation) seem t…
We consider the electonic transport in a mesoscopic metallic spin glasses. We show that the distribution of overlaps between spin configurations can be inferred from the reduction of the conductance fluctuations by the magnetic impurities. Using this property, we propose new experimental protocols to probe spin glasses directly through their overlaps.
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.
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame of extended variational principles, Derrida-Ruelle probability cascades, and overlap locking.
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.
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to the Parisi replica symmetry breaking picture of spin glasses. The finite-size scaling functions in the critical region of spin glasses below T_c in dimensions greater than 6 can be determined and for them the replica symmetric solution is unstable order by order in perturbation theory. Nevertheless the exact solution can be shown to be replica-symmetric. It i…
Ground states of 3d EA Ising spin glasses are calculated for sizes up to $14^3$ using a combination of genetic algorithms and cluster-exact approximation . The distribution $P(|q|)$ of overlaps is calculated. For increasing size the width of $P(|q|)$ converges to a nonzero value, indicating that many pure ground states exist for short range Ising spin glasses.
Anomalous Hall effect arising from the noncoplanar spin configuration (chirality) is discussed as a probe of the chiral order in spin glasses. It is shown that the Hall coefficient yields direct information about the linear and nonlinear chiral susceptibilities of the spin sector, which has been hard to obtain experimentally from the standard magnetic measurements. Based on the chirality scenario of spin-glass transition, predictions are given on the behavior of the Hall resistivity of canonical spin glasses.
The isothermal remanent magnetization is used to investigate dynamical magnetic properties of spatially three dimensional spin glasses with different spin dimensionality (Ising, XY, Heisenberg). The isothermal remanent magnetization is recorded vs. temperature after intermittent application of a weak magnetic field at a constant temperature $T_h$. We observe that in the case of the Heisenberg spin glasses, the equilibrated spin structure and the direction of the excess moment are recovered at $T_h$. The isothermal remanent magnetization thus reflects the directional character of the Dzyaloshin…
Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster updates, we show that Ising spin glasses with Levy-distributed interactions share the same universality class as Ising spin glasses with Gaussian or bimodal-distributed interactions. Corrections to scaling are large for Levy spin glasses. In order to overcome these and show that the critical exponents agree with the Gaussian case, we perform an extended scaling of the two-point finite size correlation length and the spin glass susceptibility. Furthermore, we compute the critical temperature and c…
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.
It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the lower critical dimension of the de Almeida-Thouless line in spin glasses is equal to the lower critical dimension of the large-m limit of the m-vector spin glass. Numerical studies suggest that this is close to six.
Ground states of 3d EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and Cluster-Exact Approximation. Evidence for an ultrametric structure is found by studying triplets of independent ground states where one or two values of the three overlaps are fixed.
Local minima also known as inherent structures are expected to play an essential role for the behavior of spin glasses. Here, we propose techniques to efficiently sample these configurations in Monte Carlo simulations. For the Sherrington-Kirkpatrick and the three-dimensional Edwards-Anderson model their spectra are determined and compared to analytical results.
We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian quenched random couplings. Our results clearly support the existence of replica symmetry breaking in the thermodynamical limit.
The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition. Using a ``potential function'' we follow the metastable states of the model in temperature, and discuss the possibility of level crossing (which we do not find) and multifurcation (which we find). The dynamics at a given temperature starting from an equilibrium configuration at a different temperature is also discussed. In presence of multifurcation, we find that the equilibrium is never achieved, leading to aging b…
We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.
We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast to the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.
The dependence of the transition temperature $T_g$ in terms of the concentration of magnetic impurities $c$ in spin glasses is explained on the basis of a screened RKKY interaction. The two observed power laws, $T_g ~ c$ at low $c$ and $T_g ~ c^{2/3}$ for intermediate $c$, are described in a unified approach.
Recent developments in study of two-dimensional spin glass models are reviewed in light of fractal nature of droplets at zero-temperature. Also presented are some new results including a new estimate of the stiffness exponent using a boundary condition different from conventional ones.
Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes but after allowing for fluctuation effects, a non-zero interface free energy is obtained which is significantly different from numerical expectations.
We generalize the de Almeida-Thouless line for the many-body Ising spin glass to the microcanonical ensemble and show that it coincides with the canonical one. This enables us to draw a complete microcanonical phase diagram of this model.
We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been carried out on Ising Spin Glasses in dimension three, using a technique where corrections to finite size scaling can be controled. The data show that the critical exponents vary strongly as a function of the kurtosis of the interaction distribution, a parameter which from the standard point of view should not be pertinent. This observation implies that for …
Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in applied fields. The properties of the two models are contrasted, and possible relation to experiments is discussed.
We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consisten…
Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here, we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin …
The recently proposed reduction method for diluted spin glasses is investigated in depth. In particular, the Edwards-Anderson model with \pm J and Gaussian bond disorder on hyper-cubic lattices in d=2, 3, and 4 is studied for a range of bond dilutions. The results demonstrate the effectiveness of using bond dilution to elucidate low-temperature properties of Ising spin glasses, and provide a starting point to enhance the methods used in reduction. Based on that, a greedy heuristic call ``Dominant Bond Reduction'' is introduced and explored.
We study the classical 1D Heisenberg spin glasses. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from first principles of classical mechanics lead to NP hard problem, that however in the limit of the statistical equilibrium can be calculated by P algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains' energy distribution.
We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark the presence of strong finite-size effects on the chiral sector. We find a unique phase transition for the chiral and spin glass sector, in the Universality class of Ising spin glasses. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 64x64x64 spins, over a vast range of temperatures.
We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface free-energy that is positively defined and that should scale with a positive power of the system size in the spin glass phase. In this note we study the behavior of the interface at the spin glass critical temperature $T_c$ within mean field theory. We show that the leading scaling of the interface free-energy does not depend on replica symmetry breaking, an…
We show that there is no need to modify the Parisi replica symmetry breaking ansatz, by working with $R$ steps of breaking and solving {\it exactly} the discrete stationarity equations generated by the standard ``truncated Hamiltonian" of spin glass theory.
In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will mainly considered equilibrium properties at zero magnetic field, where the situation is clear and it should be not controversial. I will present the various hypothesis at the basis of the theory and I will discuss their physical status.
The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^θ for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the addition of a scaling correction l^{-ω} in order to accurately describe droplet energies at the length scales currently probed in numerical simulations. Using this simple modification it is now possible to explain many results with the droplet model which have been found in simulations of three-dimensional Ising spin glasses.
We evaluate the corrections to the mean field values of the $x$ and the $z$ exponents at the first order in the $ε$-expansion, for $T=T_c $. We find that both $x$ and $z$ are decreasing when the space dimension decreases.
We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin correlation functions in thermalized spin configurations at low T on large lattices. We consider individual disorder samples and analyze connected clusters of very correlated sites: we analyze how the volume and the surface of these clusters increases with the lattice size. We qualify the important excitations of the system by checking how large they are, and we define a correlation length by measuring their gyration radius. We find that the clusters have a very dense interface, compatible with being space filling.
In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and of real space pictures. We highlight the f…
The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm c}$, the non-equilibrium autocorrelation decay exponent $λ_c/z_{\rm c}$, and the critical fluctuation-dissipation ratio $X_{\infty}$ all vary strongly and systematically with the form of the interaction distribution.
Large numbers of ground states of 3d EA Ising spin glasses are calculated for sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact Approximation. A detailed analysis shows that true ground states are obtained. The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t behavior with t=0.19(2) is found which strongly indicates that the 3d model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi equation for the model is written.
We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a non-analyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use First Order Reversal Curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films. We contrast our results on spin glasses to random magnets and show that…
The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states.
We derive a rigorous dynamical relation on aging phenomena -- the aging relation -- for Ising spin glasses using the method of gauge transformation. The waiting-time dependence of the auto-correlation function in the zero-field-cooling process is equivalent with that in the field-quenching process. There is no aging on the Nishimori line; this reveals arguments for dynamical properties of the Griffiths phase and the mixed phase. The present method can be applied to other gauge-symmetric models such as the XY gauge glass.
An extensive list of results for the ground state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are being tested on mean-field models at low connectivity. Comparison with existing replica results for such models verifies the strength of those techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe lattices) exhibit a richer phenomenology than has been anticipated by theory. Our data prove to be sufficiently accurate to speculate abo…
The leading term for the average height of the barriers which could separate pure states in Ising spin glasses is calculated using instanton methods. It is finite in dimensions $d < 6$. Replica symmetry breaking requires that the barriers between pure states are infinite in the thermodynamic limit, as finite barriers allow thermal mixing of pure states. As a consequence, a replica symmetry broken phase cannot survive when $d < 6$. However, for $d > 6$ no similar instanton solution exists.
This thesis pretends to be another step in the development of numerical research in disordered systems. Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical approaches. Throughout this thesis, we will discuss a variety of interesting phenomenons and we will also open new avenues to previously unexplored effects in the context of spin glasses. However, without a doubt, the leitmotiv conducting this thesis is the role of numerical simulations as a valuable tool to explore spin-glass physics. This thesis is organized int…
We introduce the technique of aspect-ratio scaling to study the scale-dependence of interfacial energies in Ising spin glasses, and we show how one can use it to determine the stiffness exponent $θ$ in a clean way, with results that are independent of the domain-wall-forcing boundary conditions imposed on the system. In space dimension d=2 we obtain $θ= -0.282(3)$ for a Gaussian distribution of exchange interactions.
New low frequency ac susceptibility measurements on two different spin glasses show that cooling/heating the sample at a constant rate yields an essentially reversible (but rate dependent) X(T) curve; a downward relaxation of X occurs during a temporary stop at constant temperature (ageing). Two main features of our results are: (i)when cooling is resumed after such a stop, X goes back to the reversible curve (chaos) (ii) upon re-heating, X perfectly traces the previous ageing history (memory). We discuss implications of our results for a real space (as opposed to phase space) picture of spin …
