On the entropy of the mean field spin glass model

TL;DR

This paper investigates the entropy behavior of the Sherrington-Kirkpatrick spin glass model, showing that its specific entropy vanishes at a critical inverse temperature derived from a functional equation involving Gibbs measures.

Contribution

It establishes a precise temperature at which the entropy of the model's Gibbs measure becomes zero, using a novel functional equation approach.

Findings

Entropy vanishes at inverse temperature β=4 log 2

Derived a functional equation relating Gibbs measures at different temperatures

Provides insight into the thermodynamic behavior of the spin glass model

Abstract

From the study of a functional equation relating the Gibbs measures at two different tempratures we prove that the specific entropy of the Gibbs measure of the Sherrington-Kirkpatrick Spin Glass Model vanishes at the inverse temperature $\beta=4 \log2$.