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Statistical Field TheoryAn Introduction to Exactly Solved Models in Statistical Physics$
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Giuseppe Mussardo

Print publication date: 2020

Print ISBN-13: 9780198788102

Published to Oxford Scholarship Online: May 2020

DOI: 10.1093/oso/9780198788102.001.0001

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Duality of the Two-dimensional Ising Model

Duality of the Two-dimensional Ising Model

(p.161) 4 Duality of the Two-dimensional Ising Model
Statistical Field Theory

Giuseppe Mussardo

Oxford University Press

Chapter 4 begins by discussing the Peierls argument, which allows us to prove the existence of a phase transition in the two-dimensional Ising model. The remaining sections of the chapter deal with duality transformations (duality in square, hexagonal and triangular lattices) that link the low- and high-temperature phases of several statistical models. Particularly important is the proof of the so-called star-triangle identity. This identity will be crucial in the later discussion of the transfer matrix of the Ising model. Finally, it covers the aspect of duality in two dimensions. An appendix provides information about the Poisson sum formula.

Keywords:   duality, low- and high-temperature expansions, Ising model, star-triangle relations, Peierls argument

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