We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.
We consider short-range Ising spin glasses in equilibrium at infinite system size, and prove that, for fixed bond realization and a given Gibbs state drawn from a suitable metastate, each translation- and locally-invariant function (for example, self-overlaps) of a single pure state in the decomposition of the Gibbs state takes the same value for all the pure states in that Gibbs state. We describe several significant applications to spin glasses.
We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-state pictures hold, the relations suggest that replica symmetry is broken as described by a Derrida-Ruelle cascade, with pure state weights distributed as a Poisson-Dirichlet process.
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with two different short-range bond distributions, the bimodal and the Gaussian ones. Through an exhaustive finite-size scaling analysis, we show that the universality class does not depend on the exact form of the bond distribution but, most important, that the quantum critical behavior is governed by an infinite randomness fixed point.
We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature $T_c$ and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length $ξ(t)$ agrees quantitatively with the predictions of a static theory, the "metastate", evaluated according to th…
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 theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states, or theories that are based infinitely many pure states-such as replica symmetry breaking-best describe realistic short-range systems. To resolve this controversy, the three-dimensional Edwards-Anderson Ising spin glass in thermal boundary conditions is studied numerically using population annealing Monte Carlo. In thermal boundary conditions all eight combinations of periodic vs antiperiodic bound…
We consider the energy difference restricted to a finite volume for certain pairs of incongruent ground states (if they exist) in the d-dimensional Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the variance of this quantity with respect to the couplings grows at least proportionally to the volume in any dimension greater than or equal to two. An essential aspect of our result is the use of the excitation metastate. As an illustration of potential applications, we use this result to restrict the possible structure of spin glass ground states in two dimensions.
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correla…
We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas of the system. We consider both short-range fluctuations associated with the local environment on Bethe lattices and long-range fluctuations that distinguish Euclidean from Bethe lattices with the same local environment. We find that the phase diagram in the temperature-coupling plane is very sensitive to the former but, at least for the $3$-dimensional (sq…
We use high temperature series expansions to study the $\pm J$ Ising spin-glass in a magnetic field in $d$-dimensional hypercubic lattices for $d=5, 6, 7$ and $8$, and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable $w=\tanh^2{J/T}$ for arbitrary values of $u=\tanh^2{h/T}$ complete to order $w^{10}$. We find that the scaling dimension $Δ$ associated with the ordering-field $h^2$ equals $2$ in the SK model and for $d\ge 6$. However, in agreement with the work of Fisher and Sompolinsky, there is a violation of scaling in a finite field, leadi…
Using inelastic neutron scattering and molecular dynamics simulations on a model Zr-Cu-Al metallic glass, we show that transverse phonons persist well into the high-frequency regime, and can be detected at large momentum transfer. Furthermore, the apparent peak width of the transverse phonons was found to follow the static structure factor. The one-to-one correspondence, which was demonstrated for both Zr-Cu-Al metallic glass and a 3-dimensional Lennard-Jones model glass, suggests a universal correlation between the phonon dynamics and the underlying disordered structure. This remarkable corre…
