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

Citation

Lin, Ming-Shr (2009) Applications of combinatorial analysis to the calculation of the partition function of the Ising Model. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05052009-133119

Abstract

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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Feynman Identity; Graph theory; Ising Model; Partition Function
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wilson, Richard M.
Thesis Committee:
  • Wilson, Richard M. (chair)
  • Wales, David B.
  • Preskill, John P.
  • Cross, Michael Clifford
Defense Date:21 April 2009
Author Email:mlin (AT) caltech.edu
Record Number:CaltechETD:etd-05052009-133119
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05052009-133119
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1641
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:14 May 2009
Last Modified:26 Dec 2012 02:40

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