Related papers: Spin glasses and the Parisi formula
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…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
I describe a class of spin models with short--range plaquette interactions whose static equilibrium properties are trivial but which display glassy dynamics at low temperatures. These models have a dual description in terms of free defects…
In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…
The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi…
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…
We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…
The Parisi formula for the free energy is among the crown jewels in the theory of spin glasses. We present a simpler proof of the lower bound in the case of the spherical mean-field model. Our method follows the TAP approach developed…
G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
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,…
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd…
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…
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking…
The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…
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…
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…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis…