The book investigated the applications of combinatorics and graph
theory in the analysis of the Feynman Identity of the partition
function of the two dimensional Ising Model. Chapter one gives a
general introduction to the partition function of the Ising Model
and the Feynman Identity in the language of graph theory. Chapter
two describes and proves combinatorially the Feynman Identity in a
special case when there is only one vertex and multiple loops.
Chapter three introduces a new way to calculate the number of
cycles in a directed graph, along with its application in the
special case discussed in chapter two to derive the analytical
expression of the number of non-periodic cycles. Chapter four comes
back to the general form of the Feynman Identity and several
combinatorial identities are derived by introducing special
conditions of the graph and applying the Feynman Identity under the
condition. Chapter five concludes the work by summarizing the main
idea in each chapter and provides insight for generalizations in
three dimensional Ising Model.
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