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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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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: 29 November 2021

Approximate Solutions

Approximate Solutions

Chapter:
(p.106) 3 Approximate Solutions
Source:
Statistical Field Theory
Author(s):

Giuseppe Mussardo

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198788102.003.0003

Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical properties of the spherical model.

Keywords:   approximate methods, mean field, Bethe–Peierls approach, random walk, spherical model

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