Related papers: From Parisi to Boltzmann
We report progress in understanding the fermionic Ising spin glass with arbitrary filling. A crossover from a magnetically disordered single band phase via two intermediate bands just below the freezing temperature to a 3-band structure at…
We propose a general scheme in which disordered systems are allowed to sacrifice energy equi-partitioning and separate into a hierarchy of ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The…
Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical…
We consider a spin system obtained by coupling two distinct Sherrington-Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the…
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed $p$-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the…
We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localised defects and effective kinetic constraints. While the thermodynamics of this system is smooth at all temperatures, we show that…
This article reviews recent years' progress in the low temperature analysis of standard models of spin glass order such as the Sherrington-Kirkpatrick (SK) model. Applications to CdTe/CdMnTe layered systems and explanation of glassy…
A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations…
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with quenched random magnetic interaction. The thermodynamics is worked out in the Full Replica Symmetry…
The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…
We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…
Michel Talagrand played a decisive role in the transformation of mean-field spin glass theory into a rigorous mathematical subject. This chapter offers a narrative account of that development. We begin with the physical origins of the…
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…
We show that fermion systems with random interactions lead to strong coupling of glassy order and fermionic correlations, which culminates in the implementation of Parisi replica permutation symmetry breaking (RPSB) in their T=0 quantum…
The variational principle (VP) has been used to capture the metastable states of a glass-forming molecular system without quenched disorder. It has been shown that VP naturally leads to a self-consistent random field Ginzburg-Landau model…
We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational representation in terms of a Parisi-type functional for the free…
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…
We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems…
The goal of this book is to present new mathematical techniques for studying the behaviour of mean-field systems with disordered interactions. We mostly focus on certain problems of statistical inference in high dimension, and on spin…