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In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…

Disordered Systems and Neural Networks · Physics 2012-07-09 YiFan Sun , Andrea Crisanti , Florent Krzakala , Luca Leuzzi , Lenka Zdeborová

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

Our goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure $p$-spin glasses above the replica…

Probability · Mathematics 2021-04-20 Gérard Ben Arous , Aukosh Jagannath

The low temperature phase of discontinuous mean-field spin glasses is characterized by the appearance of an exponential number of metastable states. Which ones among these states dominate the out-of-equilibrium dynamics of these systems? In…

Disordered Systems and Neural Networks · Physics 2009-11-10 Andrea Montanari , Federico Ricci-Tersenghi

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when…

Disordered Systems and Neural Networks · Physics 2009-11-11 Barbara Capone , Tommaso Castellani , Irene Giardina , Federico Ricci-Tersenghi

Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time…

Disordered Systems and Neural Networks · Physics 2013-01-30 Ulisse Ferrari , Luca Leuzzi , Giorgio Parisi , Tommaso Rizzo

We study a quantum extension of the spherical $p$-spin-glass model using the imaginary-time replica formalism. We solve the model numerically and we discuss two analytical approximation schemes that capture most of the features of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 Leticia F Cugliandolo , D. R. Grempel , Constantino A da Silva Santos

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 have numerically investigated the mean-field dynamics of the the $p$-spin interaction spin glass model with p=3 using an efficient method of integrating the dynamic equations. We find a new time scale associated with the onset of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 B. Kim , A. Latz

The free energy landscape of the Sherrington-Kirkpatrik (SK) Ising spin glass is simple in the framework of the Thouless-Anderson-Palmer (TAP) equations as each solution (which are minima of the free energy) has associated with it a nearby…

Disordered Systems and Neural Networks · Physics 2022-03-29 T. Aspelmeier , M. A. Moore

The barriers between metastable states near the glass transition of a random heteropolymer are studied using replicas by describing inhomogeneous states. The instanton solution for a replica space free energy functional is found numerically…

Disordered Systems and Neural Networks · Physics 2008-02-03 Shoji Takada , Peter G. Wolynes

A possible phase in short-range spin glasses exhibiting infinitely many equilibrium states is proposed and characterized in real space. Experimental signatures in equilibrating systems measured with scanning probes are discussed. Some…

Disordered Systems and Neural Networks · Physics 2007-05-23 Olivia L. White , Daniel S. Fisher

This paper investigates p-spin distributions for a generic spherical p-spin model; we give a representation of spin distributions in terms of a stochastic process. In order to do this, we find a novel double limit scheme that allows us to…

Probability · Mathematics 2019-07-10 Arka Adhikari

The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition. Using a ``potential function'' we follow the metastable…

Disordered Systems and Neural Networks · Physics 2009-10-30 A. Barrat , S. Franz , G. Parisi

The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of…

Disordered Systems and Neural Networks · Physics 2020-09-02 Giampaolo Folena , Silvio Franz , Federico Ricci-Tersenghi

The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of…

Statistical Mechanics · Physics 2007-11-08 L. S. Schulman

In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…

Disordered Systems and Neural Networks · Physics 2016-08-31 D. B. Saakian

We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…

Probability · Mathematics 2017-06-09 Wei-Kuo Chen , Partha Dey , Dmitry Panchenko

Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the configuration space in a hierarchical manner,…

Disordered Systems and Neural Networks · Physics 2009-11-11 C. Amoruso , A. K. Hartmann , M. A. Moore

We show that an 'ergodic' time scale can be extracted from the aging experiments on spin-glasses. This is the time for which a significant fraction of the metastable states have been visited. Experiments suggest that the number of…

Condensed Matter · Physics 2009-10-22 J. P. Bouchaud , E. Vincent , J. Hammann