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Related papers: Critical behavior of random spin systems

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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

The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the overlap distributions of periodic and…

Disordered Systems and Neural Networks · Physics 2017-04-05 Wenlong Wang

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the…

Statistical Mechanics · Physics 2009-10-31 E. Marinari , G. Parisi , J. J. Ruiz-Lorenzo

Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…

Condensed Matter · Physics 2009-10-22 Matteo Campellone

Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…

Condensed Matter · Physics 2007-05-23 A. Barrañón , J. A. López , C. Dorso , Fr. de L. Castillo

We consider vector spin glasses whose energy function is a Gaussian random field with covariance given in terms of the matrix of scalar products. For essentially any model in this class, we give an upper bound for the limit free energy,…

Probability · Mathematics 2021-12-06 Jean-Christophe Mourrat

The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size…

Statistical Mechanics · Physics 2009-11-10 David B. Saakian

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

Spin glasses are models of statistical mechanics in which a large number of simple elements interact with one another in a disordered fashion. One of the fundamental results of the theory is the Parisi formula, which identifies the limit of…

Probability · Mathematics 2025-10-02 Jean-Christophe Mourrat

A detailed analysis of Monte Carlo data on the two-dimensional Ising spin glass with bimodal interactions shows that the free energy of the model has a nontrivial scaling. In particular, we show by studying the correlation length that much…

Disordered Systems and Neural Networks · Physics 2009-09-29 Helmut G. Katzgraber , L. W. Lee , I. A. Campbell

In this paper we try to estimate the lower critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism…

Condensed Matter · Physics 2009-10-22 S. Franz , G. Parisi , M. A. Virasoro

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…

Probability · Mathematics 2023-08-22 Paul Balister , Béla Bollobás , Robert Morris , Paul Smith

We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi…

Probability · Mathematics 2018-03-28 Dmitry Panchenko

We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles…

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

Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap…

Statistical Mechanics · Physics 2015-06-25 H. J. Luo , L. Schuelke , B. Zheng

We consider the statistical properties over disordered samples of the overlap distribution $P_{\cal J}(q)$ which plays the role of an order parameter in spin-glasses. We show that near zero temperature (i) the {\it typical} overlap…

Disordered Systems and Neural Networks · Physics 2013-10-31 Cecile Monthus , Thomas Garel

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme…

Statistical Mechanics · Physics 2009-11-07 T. Aspelmeier , M. A. Moore

We show through a simple example that perturbations of the Hamiltonian of a spin glass which cannot be detected at the level of the free energy can completely alter the behavior of the overlap. In particular, perturbations of order O(log…

Mathematical Physics · Physics 2010-11-09 Louis-Pierre Arguin , Nicola Kistler

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed…

Statistical Mechanics · Physics 2009-11-13 Jean-Noël Aqua , Michael E. Fisher

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