A cram\'er type moderate deviation theorem for the critical curie-weiss model

TL;DR

This paper derives a Cramér-type moderate deviation theorem for the magnetization in the critical Curie-Weiss model, providing explicit error formulas using Laplace method, extending previous non-critical results.

Contribution

It introduces a direct Laplace method approach to obtain explicit error bounds for the critical Curie-Weiss model's magnetization deviations, complementing prior Stein method results.

Findings

Explicit formula for the error in the moderate deviation approximation.

A Cramér-type result for the critical Curie-Weiss model.

Methodology applicable to similar critical phenomena.

Abstract

In this paper we study the moderate deviations for the magnetization of critical Curie-Weiss model. Chen, Fang and Shao considered a similar problem for non-critical model by using Stein method. By direct and simple arguments based on Laplace method, we provide an explicit formula of the error and deduce a Cram\'er-type result.