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Related papers: The Sherrington-Kirkpatrick model for spin glasses…

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Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…

Probability · Mathematics 2007-05-23 Philippe Carmona

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…

Disordered Systems and Neural Networks · Physics 2011-10-21 A. Billoire , L. A. Fernandez , A. Maiorano , E. Marinari , V. Martin-Mayor , D. Yllanes

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of…

Statistical Mechanics · Physics 2009-11-10 Andrea Cavagna , Irene Giardina , Giorgio Parisi

We introduce a novel quantum spin-glass model, a Sherrington-Kirkpatrick model with a transverse mean-field type random magnet. We rigorously derive the exact expression of the free energy of this model at the entire parameter region. The…

Statistical Mechanics · Physics 2024-10-07 Naoto Shiraishi

The Ghatak-Sherrington (GS) spin glass model is a random probability measure defined on the configuration space $\{0,\pm1,\pm2,\ldots, \pm \mathcal{S} \}^N$ with system size $N$ and $\mathcal{S}\ge1$ finite. This generalizes the classical…

Probability · Mathematics 2024-04-03 Yueqi Sheng , Qiang Wu

We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…

Disordered Systems and Neural Networks · Physics 2015-06-24 Václav Janiš

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…

Mathematical Physics · Physics 2008-09-29 Michael Aizenman , Robert Sims , Shannon L. Starr

The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a high-temperature expansion. The resulting formula to the third order of the…

Condensed Matter · Physics 2009-10-28 Hidetoshi Nishimori , Michiko Yamana

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are…

Statistical Mechanics · Physics 2009-10-31 J. M. de Araujo , F. D. Nobre , F. A. da Costa

We discuss the issue of temperature chaos in the Sherrington--Kirkpatrick spin glass mean field model. We numerically compute probability distributions of the overlap among (equilibrium) configurations at two different values of the…

Disordered Systems and Neural Networks · Physics 2009-11-07 Alain Billoire , Enzo Marinari

We present results of a Monte Carlo study of the equilibrium dynamics of the one dimensional long-range Ising spin glass model. By tuning a parameter $\sigma$, this model interpolates between the mean field Sherrington-Kirkpatrick model and…

Disordered Systems and Neural Networks · Physics 2015-07-31 Alain Billoire

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

We study the probability distribution of the pseudo-critical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick (SK) and the Edwards-Anderson (EA) model. In both cases, we put in evidence the…

Disordered Systems and Neural Networks · Physics 2014-09-09 Michele Castellana , Aurelien Decelle , Elia Zarinelli

We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…

Probability · Mathematics 2026-03-09 Partha S. Dey , Taegu Kang

We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…

Disordered Systems and Neural Networks · Physics 2020-02-27 Maddalena Dilucca , Luca Leuzzi , Giorgio Parisi , Federico Ricci-Tersenghi , Juan J. Ruiz-Lorenzo

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable…

Statistical Mechanics · Physics 2009-11-10 Andrea Crisanti , Luca Leuzzi

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

In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…

Disordered Systems and Neural Networks · Physics 2012-12-13 Francesco Guerra

Numerical data on the probability distribution of the equilibrium relaxation time of the Sherrington-Kirkpatrick model are obtained by means of dynamical Monte Carlo simulation, for several values of the system size $N$ and temperature $T$.…

Disordered Systems and Neural Networks · Physics 2011-08-09 Alain Billoire

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