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We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

Disordered Systems and Neural Networks · Physics 2026-05-21 Yaprak Önder , Abbas Ali Saberi , Roderich Moessner

We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: 1) the averaged self-overlap converges; 2) the…

Probability · Mathematics 2023-12-27 Hong-Bin Chen

There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…

Probability · Mathematics 2018-07-30 Sourav Chatterjee

In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented results for the structure of the degenerate ground states of the three-dimensional +/- J spin glass model obtained using a genetic algorithm. In this Comment, I argue…

Disordered Systems and Neural Networks · Physics 2009-10-31 A. W. Sandvik

The Sherrington-Kirkpatrick (SK) is a foundational model for understanding spin glass systems. It is based on the pairwise interaction between each two spins in a fully connected lattice with quenched disordered interactions. The nature of…

Disordered Systems and Neural Networks · Physics 2025-06-30 Ali Talebi

We investigate the classical Renyi entropy S_n and the associated mutual information I_n in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and…

Statistical Mechanics · Physics 2016-04-26 Vincenzo Alba , Stephen Inglis , Lode Pollet

In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation…

Disordered Systems and Neural Networks · Physics 2009-11-07 Giorgio Parisi

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of…

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

We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the…

Probability · Mathematics 2023-11-21 Stephan Gufler , Adrien Schertzer , Marius A. Schmidt

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

The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. S. Dean , F. Ritort

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones…

Disordered Systems and Neural Networks · Physics 2017-02-08 Giulio Biroli , Chiara Cammarota

Following an original idea of F. Guerra, in this notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of…

Disordered Systems and Neural Networks · Physics 2013-04-10 Adriano Barra , Gino Del Ferraro , Daniele Tantari

In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA…

Disordered Systems and Neural Networks · Physics 2009-10-28 C. M. Newman , D. L. Stein

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…

Disordered Systems and Neural Networks · Physics 2013-05-29 Jack Raymond , David Saad

The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…

Disordered Systems and Neural Networks · Physics 2013-03-27 V. Janis , A. Kauch , A. Klic

We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set…

Number Theory · Mathematics 2026-01-29 Anna Chiara Lai , Paola Loreti

We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high…

Probability · Mathematics 2024-05-01 Zhou Fan , Yihong Wu

We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model…

Disordered Systems and Neural Networks · Physics 2009-10-30 L. B. Ioffe , D. Sherrington

We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…

Disordered Systems and Neural Networks · Physics 2009-11-10 V. Janis , L. Zdeborova