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Applications of Combinatorial Analysis to the Calculation of the Partition Function of the Ising Model


Lin, Ming-Shr Matt (2009) Applications of Combinatorial Analysis to the Calculation of the Partition Function of the Ising Model. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RSXD-6W47.


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
Minor Option:Business Economics and Management
Electrical Engineering
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
Record Number:CaltechETD:etd-05052009-133119
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1641
Deposited By: Imported from ETD-db
Deposited On:14 May 2009
Last Modified:26 Nov 2019 20:23

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