Applications of combinatorial analysis to the calculation of the partition function of the Ising Model

by Lin, Ming-Shr

Abstract (Summary)
The research work discussed in this thesis investigated the application of combinatorics and graph theory in the analysis of the partition function of the Ising Model. Chapter 1 gives a general introduction to the partition function of the Ising Model and the Feynman Identity in the language of graph theory. Chapter 2 describes and proves combinatorially the Feynman Identity in the special case when there is only one vertex and multiple loops. Chapter 3 digresses into the number of cycles in a directed graph, along with its application in the special case to derive the analytical expression of the number of non-periodic cycles with positive and negative signs. Chapter 4 comes back to the general case of the Feynman Identity. The Feynman Identity is applied to several special cases of the graph and a combinatorial identity is established for each case. Chapter 5 concludes the thesis by summarizing the main ideas in each chapter.
Bibliographical Information:

Advisor:Richard M. Wilson; Michael C Cross; David B. Wales; John Preskill

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis



Date of Publication:04/21/2009

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