Related papers: Replica Cluster Variational Method: the Replica Sy…
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,…
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…
In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex…
A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field…
Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is of direct relevance to combinatorial optimization and fundamental science. Search-based heuristics have difficulty with this task due to the…
The site-random Ising spin glass model is investigated. We find a rigorous symmetry for the SG correlation and the free energy, which provides some restrictions in the phase diagram. Using the defect energies calculated by the numerical…
Recent numerical simulations indicate that several different equilibrium glass transitions may be characterized by diverging correlation lengths, and that these divergences are described by a non-mean-field, Ising-like, critical exponent. I…
We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures. The main focus is on two structural glass models, SiO_2 and a Lennard-Jones system, but we also investigate a fully…
We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under…
The cluster variation - Pade` approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
We use quantum Monte Carlo methods and various analytic approximations to solve the Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We investigate the replica symmetry broken (RSB) phase of spin glass (SG) models in a random field defined on Bethe lattices at zero temperature. From the properties of the RSB solution we deduce a closed equation for the extreme values of…
The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D…
We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of…
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial…
We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value…
Zeros of the $n$th moment of the partition function $[Z^n]$ are investigated in a vanishing temperature limit $\beta \to \infty$, $n \to 0$ keeping $y=\beta n \sim O(1)$. In this limit, the moment parameterized by $y$ characterizes the…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…