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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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Fermionic Formulation of the Ising Model

Fermionic Formulation of the Ising Model

Chapter:
(p.319) 9 Fermionic Formulation of the Ising Model
Source:
Statistical Field Theory
Author(s):

Giuseppe Mussardo

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198788102.003.0009

A crucial aspect of the Ising model is its fermionic nature and this chapter is devoted to this property of the model. In the continuum limit, a Dirac equation for neutral Majorana fermions emerges. The details of the derivation are much less important than understanding why it is possible. The chapter emphasizes the simplicity and the exactness of the result, and covers the so-called Wigner-Jordan transformation, which brings the original Hamiltonian to a quadratic form in the creation and annihilation operators of the fermions. It covers the role played by the Bogoliubov transformation and the importance of the order and disorder operators.

Keywords:   Ising model, Majorana fermion, Dirac equation, transfer matrix, Hamiltonian limit

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