English
Related papers

Related papers: Mean field spin glasses treated with PDE technique…

200 papers

Answering the question of existence of efficient quantum algorithms for NP-hard problems require deep theoretical understanding of the properties of the low-energy eigenstates and long-time coherent dynamics in quantum spin glasses. We…

Disordered Systems and Neural Networks · Physics 2019-07-04 Vadim N. Smelyanskiy , Kostyantyn Kechedzhi , Sergio Boixo , Hartmut Neven , Boris Altshuler

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…

Disordered Systems and Neural Networks · Physics 2009-11-13 Adriano Barra

In previous work, we have developed a simple method to study the behavior of the Sherrington-Kirkpatrick mean field spin glass model for high temperatures, or equivalently for high external fields. The basic idea was to couple two different…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra

In this note we present an exact solution of the Monte Carlo dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We obtain the dynamical equations for a generalized set of moments which can be exactly closed. Only in a…

Condensed Matter · Physics 2009-10-28 L. L. Bonilla , F. G. Padilla , G. Parisi , F. Ritort

In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra , Fabio Lucio Toninelli

We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the…

Disordered Systems and Neural Networks · Physics 2010-09-08 K. Janzen , A. Engel , M. Mézard

The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in…

Probability · Mathematics 2016-09-21 Jinho Baik , Ji Oon Lee

The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica…

Probability · Mathematics 2015-12-23 Dmitry Panchenko

The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is…

Probability · Mathematics 2023-11-28 Erik Bates , Youngtak Sohn

In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…

Disordered Systems and Neural Networks · Physics 2008-06-10 Pedro Castro Menezes , Alba Theumann

A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model.…

Disordered Systems and Neural Networks · Physics 2013-05-28 A. Billoire , L. A. Fernandez , A. Maiorano , E. Marinari , V. Martin-Mayor , G. Parisi , F. Ricci-Tersenghi , J. J. Ruiz-Lorenzo , D. Yllanes

The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the…

Disordered Systems and Neural Networks · Physics 2025-12-11 Vincenzo Citro , Federico Ricci-Tersenghi

We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with quenched random magnetic interaction. The thermodynamics is worked out in the Full Replica Symmetry…

Statistical Mechanics · Physics 2016-08-31 Andrea Crisanti , Luca Leuzzi

The validity of the Parisi formula in the Sherrington-Kirkpatrick model (SK) was initially proved by Talagrand [18]. The central argument therein relied on a very dedicated study of the coupled free energy via the two-dimensional…

Probability · Mathematics 2016-05-16 Wei-Kuo Chen

We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking.…

Disordered Systems and Neural Networks · Physics 2022-02-21 Elena Agliari , Linda Albanese , Francesco Alemanno , Alberto Fachechi

In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…

Probability · Mathematics 2013-05-27 Dmitry Panchenko

Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…

Disordered Systems and Neural Networks · Physics 2009-11-13 K. Janzen , A. K. Hartmann , A. Engel

This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…

Disordered Systems and Neural Networks · Physics 2008-02-03 A. Barrat

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random…

Disordered Systems and Neural Networks · Physics 2009-11-10 M. Bechmann , R. Oppermann

We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…

Disordered Systems and Neural Networks · Physics 2009-11-10 A. Crisanti , L. Leuzzi