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Related papers: Beyond the Sherrington-Kirkpatrick Model

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From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the…

Mathematical Physics · Physics 2010-07-26 Flora Koukiou

Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington-Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass…

Statistical Mechanics · Physics 2023-12-05 Atanu Rajak , Bikas K Chakrabarti

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…

Statistical Mechanics · Physics 2014-01-13 Ioannis A. Hadjiagapiou

The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…

Probability · Mathematics 2007-12-18 Sourav Chatterjee

Based on the modified Thouless-Anderson-Palmer equations a detailed numerical investigation for the complexity of the Sherrington-Kirkpatrick spin glass is worked out. The data suggest a scaling law which leads to a vanishing of the…

Disordered Systems and Neural Networks · Physics 2007-05-23 T. Plefka

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

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

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 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

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

In his Comment, Krakoviack [Phys. Rev. B (2007)] finds that the phase behavior of the s+p spin-glass model is different from what proposed by Crisanti and Leuzzi [Phys. Rev. B 73, 014412 (2006)] if s and p are larger than two and are…

Disordered Systems and Neural Networks · Physics 2009-11-13 A. Crisanti , L. Leuzzi

We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…

Statistical Mechanics · Physics 2009-11-10 Alain Billoire , Barbara Coluzzi

Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…

Disordered Systems and Neural Networks · Physics 2009-11-13 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

We consider a finite range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance $\gamma^{-1}$. We show that, under mild assumptions on the interaction potential, the…

Statistical Mechanics · Physics 2009-11-10 Silvio Franz , Fabio Lucio Toninelli

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…

Disordered Systems and Neural Networks · Physics 2023-12-01 Ada Altieri , Marco Baity-Jesi

We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 E. Marinari

These notes give an introduction to the physics of the infinite range version of the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model. In a first part, I motivate and introduce the Edwards--Anderson and…

Disordered Systems and Neural Networks · Physics 2007-10-18 Alain Billoire

In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on…

Disordered Systems and Neural Networks · Physics 2009-11-13 Giorgio Parisi

Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models,…

Probability · Mathematics 2025-11-10 Elizabeth Collins-Woodfin , Han Gia Le