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Advanced Statistical Mechanics$
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Barry M McCoy

Print publication date: 2009

Print ISBN-13: 9780199556632

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199556632.001.0001

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Ising model spontaneous magnetization and form factors

Ising model spontaneous magnetization and form factors

Chapter:
(p.363) 12 Ising model spontaneous magnetization and form factors
Source:
Advanced Statistical Mechanics
Author(s):

Barry M. McCoy

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199556632.003.0012

This chapter develops and uses the theory of Wiener–Hopf sum equations to derive Szegö's theorem. This theorem is used to compute the spontaneous magnetization of the Ising model. The Wiener–Hopf methods are then used to compute the form factor expansion on the correlation functions and this expansion is used to derive the behaviour of the two-point function at large separations. These expansions give a microscopic description of the critical point and provide the basis of the scaling phenomenology presented in Chapter 4. It is explained how to use symbolic computer computations to discover Fuchsian differential equations for the diagonal correlations.

Keywords:   Wiener–Hopf sum equations, Szegö's theorem, spontaneous magnetization, form factor expansions, expansions, symbolic computer computations

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