The Representation Of Parisi Functional In The Mixed P-spin Models Based On The Ruelle Probability Cascades

In this master dissertation, We use the background knowledge of spin glass model, SK model, p-spin model, Poisson process, etc.. and obtain the representation of Parisi functional in the mixed p-spin models based on the Ruelle probability cascades. This paper is divided into five chapters:In chapter 1, we introduce the background and status of this paper.In chapter 2, we introduce the preliminary knowledge, including the background knowledge of spin glass model, SK model, p-spin model.In chapter 3, we discusse Poisson process and Poisson Dirichlet process.In chapter 4, considering the Poisson process and the Poisson Dirichlet process, we deduce the Ruelle probability cascades, and obtain several important construc-tion properties.In chapter 5, we stydy the mixed p-spin models, using the last chapter's prop-erties obtain the representation theory of Parisi functional.