Correlations, Long Range Order and Dimensionality
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Published:1983
Issue:5
Volume:36
Page:683
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ISSN:0004-9506
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Container-title:Australian Journal of Physics
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language:en
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Short-container-title:Aust. J. Phys.
Abstract
After a retrospective look at the nature of correlations in the case of the helium A transition, we consider long range correlations and their information content for critical phenomena in general. Separation of the statistical from the geometric information leads to the resolution of a long-standing dilemma concerning the dimensionality dependence of the hyper-scaling relations. The hyper-scaling inequalities are the result of the significant correlations suffering a re-arrangement when a regular contribution dominates the singular part of the free energy. The inequalities can each be replaced by a pair of equalities. This resolution has a bearing on the special place of four dimensions as the origin for the e-expansion technique of the renormalization group approach.
Publisher
CSIRO Publishing
Subject
General Physics and Astronomy