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In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field…

Mathematical Physics · Physics 2021-04-14 Roberto Vila

The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its…

Statistical Mechanics · Physics 2015-12-01 Fabrizio Antenucci , Andrea Crisanti , Luca Leuzzi

The random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and that their statistics satisfy the predictions of the…

Disordered Systems and Neural Networks · Physics 2024-08-28 Bernard Derrida , Peter Mottishaw

We study the free energy of a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean, we show that the thermodynamic limit of the quenched free…

Probability · Mathematics 2022-12-06 Aukosh Jagannath , Patrick Lopatto

In two papers Franz, Leone and Toninelli proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution [5] and a general distribution [6]. Panchenko and Talagrand [16] simplified…

Probability · Mathematics 2018-03-14 Marc Lelarge , Mendes Oulamara

This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…

Probability · Mathematics 2022-04-05 David Belius

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…

Mathematical Physics · Physics 2014-07-09 Gernot Akemann , Dario Villamaina , Pierpaolo Vivo

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

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue…

Probability · Mathematics 2018-10-25 Louis-Pierre Arguin , Warren Tai

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 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

While the Gibbs states of spin glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying ``quenched state''. The assumption of such continuity in…

Statistical Mechanics · Physics 2015-06-25 M. Aizenman , P. Contucci

We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the…

Disordered Systems and Neural Networks · Physics 2009-10-30 Andrea Cavagna , Irene Giardina , Giorgio Parisi

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories…

Statistical Mechanics · Physics 2009-11-07 Alain Barrat , Ludovic Berthier

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…

Disordered Systems and Neural Networks · Physics 2007-05-23 Elmar Bittner , Wolfhard Janke

We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution of the Sherrington-Kirkpatrick and 3D Edwards-Anderson models of Ising spin glasses. We find that this…

Disordered Systems and Neural Networks · Physics 2014-09-16 A. Billoire , A. Maiorano , E. Marinari , V. Martin-Mayor , D. Yllanes

We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component…

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

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…

Statistical Mechanics · Physics 2009-02-02 Silvio Franz , T Jorg , Giorgio Parisi

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

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of…

Disordered Systems and Neural Networks · Physics 2010-07-26 Shimul Akhanjee , Joseph Rudnick