A Cramer type moderate deviation theorem for the critical Curie-Weiss model

Limit theorems for the magnetization of Curie-Weiss model have been studied extensively by Ellis and Newman. To refine these results, Chen, Fang and Shao prove Cramer type moderate deviation theorems for non-critical cases by using Stein method. In this paper, we consider the same question for the remaining case-the critical Curie-Weiss model. By direct and simple arguments based on Laplace method, we provide an explicit formula of the error and deduce a Cramer type result.