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
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|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||21 April 2009|
|Author Email:||mlin (AT) caltech.edu|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||14 May 2009|
|Last Modified:||26 Dec 2012 02:40|
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