Expectation Difference Under Different Probability Measures And Application

Ising Model has been the research subject of many scholars since it was put forward in1920 due to its intuitive form and rich connotation.Ising Model was initially used to study ferromagnetism and phase transition process.Then it was abstracted into a simple statistical model and was applied to various fields.Since its invention,it has been showing its rich connotation and significance.The purpose of this paper is to explore the differences between different Ising Models through theoretical and numerical simulations.First,by using Stein Method,Poisson's Equation and Glauber Dynamics,we give the conclusion that the expected difference of a general function under two probability measures can be controlled.Second,we present the definition of Ising Model.Third,we give the specific forms and related conclusions of the differences between different Ising Models.Finally,we develop a simulation algorithm to study and verify the above conclusions numerically.