Bookcover of Combinatorics and the Feynman Identity
Booktitle:

Combinatorics and the Feynman Identity

Applications of Combinatorial Analysis to the Feynman Identity

VDM Verlag Dr. Müller (2009-07-17 )

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ISBN-13:

978-3-639-17821-0

ISBN-10:
3639178211
EAN:
9783639178210
Book language:
English
Blurb/Shorttext:
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.
Publishing house:
VDM Verlag Dr. Müller
Website:
http://www.vdm-verlag.de
By (author) :
MINGSHR LIN
Number of pages:
52
Published on:
2009-07-17
Stock:
Available
Category:
Mathematics
Price:
49.00 €
Keywords:
Feynman Identity, Combinatorics, graph theory, Partition Function, Ising Model, statistical mechanics, Square Lattice, Cycles, Paths, Sign function

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