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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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High temperature expansions for magnets at H = 0

High temperature expansions for magnets at H = 0

(p.232) 9 High temperature expansions for magnets at H = 0
Advanced Statistical Mechanics

Barry M. McCoy

Oxford University Press

This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this data is used to estimate critical exponents. In dimension two the three-component model exhibits what in field theory is called ‘asymptotic freedom’ where the critical temperature is at T = 0. The corresponding analysis is done for the quantum Heisenberg model and universality with respect to the quantum spin is evaluated. A discussion of the relation between statistical mechanics and quantum field theory is given.

Keywords:   high temperature expansions, component spin models, Heisenberg model, critical exponents, asymptotic freedom, quantum field theory

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