Fluctuation of free energy for the mean-field Ghatak-Sherrington Model

TL;DR

This paper proves a central limit theorem for the free energy in the mean-field Ghatak-Sherrington model at high temperatures, extending stochastic calculus methods from the SK model.

Contribution

It introduces a generalized stochastic calculus approach to establish a CLT for the free energy in the Ghatak-Sherrington model at high temperatures.

Findings

Central limit theorem for free energy at high temperatures

Extension of stochastic calculus methods to Ghatak-Sherrington model

Analytical proof based on generalized stochastic calculus

Abstract

In this short note, we prove a central limit theorem for the free energy in the Ghatak- Sherrington model at high enough temperatures, based on a generalization of the stochastic calculus method for the SK model derived in [CN95, Tin05].