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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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The Ising model in two dimensions: summary of results

The Ising model in two dimensions: summary of results

(p.277) 10 The Ising model in two dimensions: summary of results
Advanced Statistical Mechanics

Barry M. McCoy

Oxford University Press

This chapter summarizes the many results of the exactly solved Ising model in two dimensions at H = 0 including: the partition function, free energy, spontaneous magnetization, the Toeplitz determinant representations of the correlation functions, the Painlevé VI differential equation for the diagonal two spin correlations, the form factor expansion of the magnetic susceptibility, the scaling limit, the boundary properties of the half plane lattice, and the random layered lattice. For H ≠ 0 the Lee-Yang circle theorem, the free energy and magnetization for H/kBT = iπ/2 expansions for small H, the results of Zamolodchikov at T = Tc and a discussion of extended analyticity are given.

Keywords:   Ising model, partition function, spontaneous magnetization, Painlevé, Toeplitz determinants, Lee–Yang circle theorem, random layered lattice, boundary properties

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