This thesis is composed of two major parts. The first major part includes the first two chapters. In Chapter 1, we go over the history and background of spin glass theory and introduce the Sherrington-Kirkpatrick (SK) model and the Ghatak-Sherrington (GS) model. In Chapter 2, we introduce the Thouless-Anderson-Palmer (TAP) equations and review some related literature in both physics and mathematics. The second major part consists of the last two chapters, which are devoted to studyingthe TAP equations for the GS model. In Chapter 3, we derive the TAP equations for the GS model [36], which con rms the prediction of [86]. In the last chapter, we construct an iterative approximation scheme for solutions of the TAP equations for the GS model and show the iteration converges to the local magnetization under high temperature.

Creator

• Chen, Xi

DOI

• https://doi.org/10.21985/n2-wn68-4957

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16090
• etdadmin_upload_903175

Keyword

• Probability
• Spin Glass

Date created

• 2022-01-01

Resource type

• Dissertation

Rights statement

• In Copyright