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During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick…

Disordered Systems and Neural Networks · Physics 2015-05-18 Adriano Barra , Aldo Di Biasio , Francesco Guerra

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…

Disordered Systems and Neural Networks · Physics 2009-10-30 R. Baviera , M. Pasquini , M. Serva

We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…

Disordered Systems and Neural Networks · Physics 2016-08-31 Luca De Sanctis

Jagannath and Tobasco~\cite{JagTob} proposed a generalized de Almeida-Thouless (AT) criterion aimed at characterizing the replica symmetric (RS) regime for a broad class of mixed \(p\)-spin glass models with Ising spins. In this paper, we…

Probability · Mathematics 2026-02-05 Jean-Christophe Mourrat , Adrien Schertzer

We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of…

Mathematical Physics · Physics 2012-05-18 Adriano Barra , Giuseppe Genovese , Francesco Guerra , Daniele Tantari

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo meanfield Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction…

Disordered Systems and Neural Networks · Physics 2025-06-18 Soumyaditya Das , Soumyajyoti Biswas , Bikas K. Chakrabarti

The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…

Disordered Systems and Neural Networks · Physics 2008-03-25 Helmut G. Katzgraber , Alexander K. Hartmann , A. P. Young

We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…

Disordered Systems and Neural Networks · Physics 2012-10-31 Giorgio Parisi , Tommaso Rizzo

We investigate the classical Renyi entropy S_n and the associated mutual information I_n in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and…

Statistical Mechanics · Physics 2016-04-26 Vincenzo Alba , Stephen Inglis , Lode Pollet

In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…

Disordered Systems and Neural Networks · Physics 2012-12-13 Francesco Guerra

The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical…

Disordered Systems and Neural Networks · Physics 2012-10-29 B. Yucesoy , Helmut G. Katzgraber , J. Machta

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of…

Statistical Mechanics · Physics 2009-11-10 Andrea Cavagna , Irene Giardina , Giorgio Parisi

We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy…

Mathematical Physics · Physics 2026-03-10 Anouar Kouraich , Chokri Manai , Simone Warzel

The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the…

Disordered Systems and Neural Networks · Physics 2022-04-20 Francesco Camilli , Pierluigi Contucci , Emanuele Mingione

We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…

Probability · Mathematics 2020-04-17 Gérard Ben Arous , Aukosh Jagannath

We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…

Condensed Matter · Physics 2009-10-22 A. C. C Coolen , D. Sherrington

We consider the free energy of the bipartite spherical Sherrington--Kirkpatrick model. We find the critical temperature and prove the limiting free energy for all non-critical temperature. We also show that the law of the fluctuation of the…

Probability · Mathematics 2017-11-20 Jinho Baik , Ji Oon Lee

This paper studies spin glass to paramagnetic transition in the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J$ and inverse temperature $\beta$. The disorder of the system is…

Probability · Mathematics 2024-08-26 Iain M. Johnstone , Yegor Klochkov , Alexei Onatski , Damian Pavlyshyn

We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L^3 spins. After averaging over large sets of EA system samples of 3 =< L =< 10, we obtain accurate numbers for distributions p(q) of the overlap…

Disordered Systems and Neural Networks · Physics 2013-04-30 J. F. Fernández , J. J. Alonso

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…

Disordered Systems and Neural Networks · Physics 2012-10-31 Tommaso Rizzo