Real spin glasses relax slowly in the shade of hierarchical trees

TL;DR

This paper reviews experimental evidence supporting the relevance of the mean-field spin glass theory, especially the Parisi solution, to real spin glasses, highlighting key phenomena like phase transition, susceptibility behavior, and ultrametric symmetry.

Contribution

It provides a comprehensive overview connecting mean-field theory predictions with experimental results and discusses extensions beyond mean-field in real spin glasses.

Findings

Confirmation of phase transition and susceptibility behavior predicted by theory

Agreement of fluctuation dissipation ratio with noise measurements

Ultrametric symmetry explains rejuvenation and memory effects

Abstract

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview of the important experimental results which could be understood within the mean-field solution. The existence of a true phase transition and the particular behaviour of the susceptibility below the freezing temperature, predicted by the theory, are clearly confirmed by the experimental results. The behaviour of the complex order parameter and of the Fluctuation Dissipation ratio are in good agreement with results of spontaneous noise measurements. The very particular ultrametric symmetry, the key feature of the theory, provided us with a simple description of the rejuvenation and memory effects observed in experiment. Finally, going a step beyond mean-field, the paper shortly discusses new analyses in terms of correlated domains characterized by their length scales, as well as new experiments on superspin glasses which compare well with recent theoretical simulations.