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We prove the existence of full replica symmetry breaking (FRSB) for the Sherrington-Kirkpatrick (SK) model at low temperature. More specifically, we prove that slightly beyond the critical temperature, the Parisi measure for the SK model is…

Probability · Mathematics 2025-04-17 Yuxin Zhou

We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be…

Disordered Systems and Neural Networks · Physics 2011-02-28 A. Crisanti , C. De Dominicis

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a…

Probability · Mathematics 2021-06-18 Antonio Auffinger , Wei-Kuo Chen , Qiang Zeng

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from…

Disordered Systems and Neural Networks · Physics 2009-11-07 A. Crisanti , T. Rizzo

In this note we study the zero temperature dynamics of the Sherrington Kirkppatric model and we investigate the statistical properties of the configurations that are obtained in the large time limit. We find that the replica symmetry is…

Condensed Matter · Physics 2007-05-23 Giorgio Parisi

To test the stability of the Parisi solution near T=0, we study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field…

Disordered Systems and Neural Networks · Physics 2011-02-28 A. Crisanti , C. De Dominicis

Some recent results concerning the Sherrington-Kirkpatrick model are reported. For $T$ near the critical temperature $T_c$, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in…

Disordered Systems and Neural Networks · Physics 2011-11-03 A. Crisanti , C. De Dominicis

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…

Disordered Systems and Neural Networks · Physics 2008-09-16 V. Janis , A. Klic

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of…

Disordered Systems and Neural Networks · Physics 2008-09-16 V Janis , A. Klic , M. Ringel

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…

Disordered Systems and Neural Networks · Physics 2014-10-29 Matthew Wittmann , B. Yucesoy , Helmut G. Katzgraber , J. Machta , A. P. Young

An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is…

Disordered Systems and Neural Networks · Physics 2011-02-28 A. Crisanti , C. De Dominicis

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

We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…

Disordered Systems and Neural Networks · Physics 2009-11-10 V. Janis , L. Zdeborova

We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature…

Disordered Systems and Neural Networks · Physics 2013-05-29 Manuel J. Schmidt , Reinhold Oppermann

A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite…

Disordered Systems and Neural Networks · Physics 2009-11-13 Reinhold Oppermann , Manuel J. Schmidt

We develop a simple method to study the high temperature, or high external field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push…

Disordered Systems and Neural Networks · Physics 2009-11-07 Francesco Guerra , Fabio L. Toninelli

We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…

Statistical Mechanics · Physics 2009-11-10 Alain Billoire , Barbara Coluzzi

We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems…

Statistical Mechanics · Physics 2009-10-31 A. C. C. Coolen , J. van Mourik

The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…

Disordered Systems and Neural Networks · Physics 2013-03-27 V. Janis , A. Kauch , A. Klic

In a recent work (Eissfeller and Opper, 1992) a numerical method has been proposed to simulate off-equilibrium zero-temperature parallel dynamics for the SK model without finite size effects. We study the extension of the method to non-zero…

Condensed Matter · Physics 2007-05-23 Giovanni Ferraro
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