Related papers: Spin Glasses
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…
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…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…
We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the…
We study the four dimensional Gaussian spin glass in presence of a magnetic field. Using off-equilibrium numerical simulations we have found that the probability distribution of the overlaps is built in the same way as that of the Mean…
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.…
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$…
In this paper we review some recent rigorous results that provide an essentially complete solution of a class of spin glass models introduced by Derrida in the 1980ies. These models are based on Gaussian random processes on $\{-1,1\}^N$…
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…
We show that the predictions of spontaneously broken replica symmetry are in perfect agreement with the recent rigorous results obtained by Newman and Stein.
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica…
In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…
The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of…
Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…
This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial…
Simulational studies of spin glasses in the last decade have focussed on the so-called replicon exponent $\alpha$ as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking…
The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the…
In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…
We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full…