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Related papers: Parisi formula for balanced Potts spin glass

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We consider the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. the exponentially small probability of finding a system with intensive free energy smaller…

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

We consider the spherical mixed $p$-spin models and investigate the structure of the Parisi measure at zero temperature. We prove that for the spherical spin models with $n$ components, the Parisi measure at zero temperature is at most…

Probability · Mathematics 2023-03-10 Yuxin Zhou

We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational representation in terms of a Parisi-type functional for the free…

Probability · Mathematics 2014-02-11 Anton Klimovsky

We present extended versions and give detailed proofs of results concerning percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given…

Disordered Systems and Neural Networks · Physics 2011-11-10 J. Machta , C. M. Newman , D. L. Stein

We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures. The main focus is on two structural glass models, SiO_2 and a Lennard-Jones system, but we also investigate a fully…

Statistical Mechanics · Physics 2007-05-23 Walter Kob , Claudio Brangian , Torsten Stuhn , Ryoichi Yamamoto

We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…

Probability · Mathematics 2017-06-09 Wei-Kuo Chen , Partha Dey , Dmitry Panchenko

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically…

Disordered Systems and Neural Networks · Physics 2009-11-07 Tommaso Rizzo

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 determine the structure of the Parisi measure at zero temperature for the spherical p+s spin glass model. We show that depending on the values of p and s, four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as…

Probability · Mathematics 2022-09-09 Antonio Auffinger , Yuxin Zhou

We study a finite range spin glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance $\gamma^{-1}$. We prove that, under a positivity condition for the interaction potential,…

Disordered Systems and Neural Networks · Physics 2009-11-10 Silvio Franz , Fabio Lucio Toninelli

We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in…

Ground states of Ising spin glasses on fully connected graphs are studied for a broadly distributed bond family. In particular, bonds $J$ distributed according to a Levy distribution P(J)\propto 1/|J|^{1+\alpha}, |J|>1, are investigated for…

Disordered Systems and Neural Networks · Physics 2014-11-25 S. Boettcher

We show that color symmetry is preserved at high temperatures in the Potts spin glass model with $\kappa \ge 3$ colors. Our proof employs the second moment method applied to the balanced model with a suitable centering of the Hamiltonian,…

Probability · Mathematics 2026-03-03 Heejune Kim

In this paper we develop a method introduced by one of us to study metastable states in spin glasses. We consider a `potential function' defined as the free energy of a system at a given temperature $T$ constrained to have a fixed overlap…

Condensed Matter · Physics 2009-10-28 S. Franz , G. Parisi

We present the results of Monte Carlo simulations of two different Potts glass models with short range random interactions. In the first model a \pm J-distribution of the bonds is chosen, in the second model a Gaussian distribution. In both…

Statistical Mechanics · Physics 2009-11-07 Claudio Brangian , Walter Kob , Kurt Binder

The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd…

Probability · Mathematics 2012-04-24 Wei-Kuo Chen

In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the…

Disordered Systems and Neural Networks · Physics 2020-05-14 Manaka Okuyama , Masayuki Ohzeki

Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a…

Statistical Mechanics · Physics 2009-11-07 Bernd A. Berg , Alain Billoire , Wolfhard Janke

We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with $D$ species, the Parisi formula is known to be valid, and expresses the limit free energy as a supremum over monotone…

Probability · Mathematics 2025-08-11 Hong-Bin Chen , Victor Issa , Jean-Christophe Mourrat

In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap.…

Disordered Systems and Neural Networks · Physics 2018-12-18 Liming Pan , Simone Franchini