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Related papers: A Friendly Tutorial on Mean-Field Spin Glass Techn…

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We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed…

Disordered Systems and Neural Networks · Physics 2015-05-08 G. Parisi , F. Ricci-Tersenghi , D. Yllanes

Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…

Statistical Mechanics · Physics 2014-05-29 Smarajit Karmakar , Giorgio Parisi

We consider the Ising spin glass for the arbitrary spin S with the short- ranged interaction using the Bethe- Peierls approximation previously formulated by Serva and Paladin for the same system but limited to S=1/2. Results obtained by us…

Disordered Systems and Neural Networks · Physics 2009-10-31 K. Walasek , K. Lukierska- Walasek , M. Wodawski

These are expanded notes for a short series of lectures, presented at the University of Luxembourg in 2017, giving an introduction to some of the ideas of supersymmetry and supergeometry. In particular, we start from some motivating facts…

Differential Geometry · Mathematics 2025-01-07 Andrew James Bruce

We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials…

Disordered Systems and Neural Networks · Physics 2016-11-23 N. Kawashima , H. Rieger

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field--temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first…

Disordered Systems and Neural Networks · Physics 2008-05-13 Thomas Jorg , Helmut G. Katzgraber , Florent Krzakala

This is a short review on the compatibility between (a) mean-field, mode-coupling theories of the glass transition, where potential energy landscape ideas are natural, and (b) the necessity of describing the slowing down of glassy materials…

Soft Condensed Matter · Physics 2007-05-23 Jean-Philippe Bouchaud

We study the ultrametric structure of phase space of one-dimensional Ising spin glasses with random power-law interaction in an external random field. Although in zero field the model in both the mean-field and non-mean-field universality…

Disordered Systems and Neural Networks · Physics 2012-11-07 Helmut G. Katzgraber , Thomas Jorg , Florent Krzakala , Alexander K. Hartmann

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly…

Disordered Systems and Neural Networks · Physics 2010-05-12 L. A. Fernandez , V. Martin-Mayor , G. Parisi , B. Seoane

I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder…

Disordered Systems and Neural Networks · Physics 2008-02-03 E. Marinari

In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating…

Disordered Systems and Neural Networks · Physics 2007-05-23 Victor Dotsenko

Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…

Statistical Mechanics · Physics 2023-05-03 Leticia F. Cugliandolo

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…

Machine Learning · Statistics 2025-04-18 Zohar Ringel , Noa Rubin , Edo Mor , Moritz Helias , Inbar Seroussi

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

After a rapid introduction to the physical motivations and a succinct presentation of heuristic results, this survey summarises the main mathematical results known on the Edwards-Anderson and the Sherrington-Kirkpatrick models of spin…

Condensed Matter · Physics 2007-05-23 Dimitri Petritis

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

Probability · Mathematics 2008-05-08 Robert J Adler

This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra

We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension…

Disordered Systems and Neural Networks · Physics 2013-05-29 Auditya Sharma , A. P. Young

Spin relaxation close to the glass temperature of CuMn and AuFe spin glasses is shown, by neutron spin echo, to follow a generalised exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic…

Disordered Systems and Neural Networks · Physics 2009-02-25 R M Pickup , R Cywinski , C Pappas , B Farago , P Fouquet

Comparisons and analogies are drawn between materials ferroic glasses and conventional spin glasses, in terms of both experiment and theoretical modelling, with inter-system conceptual transfers leading to suggestions of further issues to…

Disordered Systems and Neural Networks · Physics 2019-09-04 David Sherrington