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Related papers: Spherical spin glass model with external field

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We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full…

Disordered Systems and Neural Networks · Physics 2015-06-12 Francesco Guerra

We consider the spherical spin glass model defined by a combination of the pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian and the ferromagnetic Curie-Weiss Hamiltonian. In the large system limit, there is a two-dimensional phase…

Probability · Mathematics 2018-10-17 Jinho Baik , Ji Oon Lee , Hao Wu

20 years ago, Bovier, Kurkova, and L\"owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we…

Probability · Mathematics 2022-05-31 Anton Bovier , Adrien Schertzer

We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the…

Probability · Mathematics 2018-03-28 Jinho Baik , Ji Oon Lee

Binary mixtures of large and small particles with disparate size ratio exhibit a rich phenomenology at their glass transition points. In order to gain insights on such systems, we introduce and study a two-component version of the $p$-spin…

Disordered Systems and Neural Networks · Physics 2016-08-03 Harukuni Ikeda , Atsushi Ikeda

We consider a spin system obtained by coupling two distinct Sherrington-Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the…

Probability · Mathematics 2013-10-04 Wei-Kuo Chen

We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…

Statistical Mechanics · Physics 2007-10-25 Luca De Sanctis , Adriano Barra , Viola Folli

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

The state of art in spin glass field theory is reviewed.

Statistical Mechanics · Physics 2008-02-03 C. De Dominicis , I. Kondor , T. Temesvari

We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…

Disordered Systems and Neural Networks · Physics 2009-11-10 A. Crisanti , L. Leuzzi

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…

Condensed Matter · Physics 2009-11-07 E. Brézin , C. De Dominicis

We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach…

Statistical Mechanics · Physics 2009-10-30 Francesco M. Russo

The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…

Disordered Systems and Neural Networks · Physics 2026-03-11 Theodorus Maria Nieuwenhuizen

In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…

Disordered Systems and Neural Networks · Physics 2009-11-11 Tommaso Castellani , Andrea Cavagna

We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…

Disordered Systems and Neural Networks · Physics 2025-08-27 Stefan Boettcher , Ginger E. Lau

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

We study the correlations between two equilibrium states of SK spin glasses at different temperatures or magnetic fields. The question, presiously investigated by Kondor and Kondor and V\'egs\"o, is approached here constraining two copies…

Condensed Matter · Physics 2009-10-22 S. Franz , M. Ney-Nifle

We study the problem of glassy relaxations in the presence of an external field in the highly controlled context of a spin-glass simulation. We consider a small spin glass in three dimensions (specifically, a lattice of size L=8, small…

Disordered Systems and Neural Networks · Physics 2019-03-08 I. Gonzalez-Adalid Pemartin , V. Martin-Mayor , G. Parisi , J. J. Ruiz-Lorenzo

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

Ground states of the three dimensional Edwards-Anderson spin glass are computed in the presence of an external magnetic field. Our algorithm is sufficiently powerful for us to treat systems with up to 600 spins. We perform a statistical…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. Houdayer , O. C. Martin