Jump to ContentJump to Main Navigation
Statistical Field TheoryAn Introduction to Exactly Solved Models in Statistical Physics$
Users without a subscription are not able to see the full content.

Giuseppe Mussardo

Print publication date: 2020

Print ISBN-13: 9780198788102

Published to Oxford Scholarship Online: May 2020

DOI: 10.1093/oso/9780198788102.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 01 December 2021

Fermionic Formulation of the Ising Model

Fermionic Formulation of the Ising Model

(p.319) 9 Fermionic Formulation of the Ising Model
Statistical Field Theory

Giuseppe Mussardo

Oxford University Press

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .