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Physical review. B, Solid state

Logarithmic Corrections to the Molecular-Field Behavior of Critical and Tricritical Systems

Franz Wegner, Eberhard K. Riedel

Published Jan 1, 1973• 335 citations
Publisher

Abstract

The asymptotic critical form of thermodynamic functions is analyzed by means of renormalization-group techniques. If certain exponent relations are satisfied, then the critical behavior is not described by a simple power law, but a power law multiplied by a fractional power of a logarithm. The approach is applied to two special systems whose critical exponents are molecular-field-like. (i) For ordinary critical transitions in four dimensions we find the same logarithmic factors previously computed by Larkin and Khmel'nitskii. (ii) For tricritical transitions in three dimensions we compute the logarithmic corrections to the molecularfield tricritical behavior discussed in an earlier publication.

DOI
10.1103/physrevb.7.248

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We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range φ n -theories) and below it.This allows us to check the scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and Fisher zeroes) of these models.Moreover, we have obtained an explicit method to compute the ϙ exponent [defined by ξ ∼ L(log L) ϙ] and, finally, we have found a new derivation of the scaling law associated with it.
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