Deterministic spin models with a glassy phase transition

TL;DR

This paper introduces deterministic infinite-range spin models derived from chaotic maps, predicting a glassy phase transition at a specific critical temperature through mean field equations.

Contribution

It presents a novel class of deterministic spin models with a glassy phase transition, derived from chaotic map quantization, and analyzes their mean field behavior.

Findings

Prediction of a glassy phase transition at T~0.8

Derivation of TAP equations for the models

Identification of a glassy phase in deterministic spin systems

Abstract

We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperature expansion. They predict a glassy phase transition at the critical temperature $T\sim 0.8$.