Related papers: Spectral gap estimates in mean field spin glasses
We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…
Metastable states in Ising spin-glass models are studied by finding iterative solutions of mean-field equations for the local magnetizations. Two different equations are studied: the TAP equations which are exact for the SK model, and the…
A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower…
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
We study Glauber dynamics for sampling from discrete distributions $\mu$ on the hypercube $\{\pm 1\}^n$. Recently, techniques based on spectral independence have successfully yielded optimal $O(n)$ relaxation times for a host of different…
Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be…
We present a simple strategy to derive universal bounds on the spectral gap of reversible stochastic exchange models on arbitrary graphs. The Kipnis-Marchioro-Presutti (KMP) model, the harmonic process (HP), and the immediate exchange model…
The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…
We study the distribution of overlaps of glassy minima, taking proper care of residual symmetries of the system. Ensembles of locally stable, low lying glassy states are efficiently generated by rapid cooling from the liquid phase which has…
The study of the low temperature phase of spin glass models by means of Monte Carlo simulations is a challenging task, because of the very slow dynamics and the severe finite size effects they show. By exploiting at the best the…
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse…
We consider spin systems on the integer lattice graph $\mathbb{Z}^d$ with nearest-neighbor interactions. We develop a combinatorial framework for establishing that exponential decay with distance of spin correlations, specifically the…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing of the…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link…
We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full…