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Progress of Theoretical Physics

Critical Behavior of an Extremely Anisotropic n-Vector Model

S. Hikami

Published Nov 1, 1974• 6 citations
Publisher

Abstract

The critical behavior of m-vector-like n-vector model is studied in the large n limit (m/n = 0) by 1/n expansion. In this limit, mean-field bahavior is obtained. For finite n, critical behavior becomes like m-vector. The crossover from mean-field behavior to m-vector-like behavior is considered in 1/n and 1/m expansions.
DOI
10.1143/ptp.52.1431

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The critical behavior of a system of nnn-component classical "spins"with anisotropic pair interactions is discussed using renormalization-group techniques for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$. To first order in $\ensuremath{\epsilon}$ the correlation and susceptibility exponents in the isotropic limit are $2\ensuremath{\nu}=\ensuremath{\gamma}=1+[\frac{(n+2)}{2(n+8)}]\ensuremath{\epsilon}$, while the anisotropy or crossover exponent is $\ensuremath{\varphi}=1+[\frac{n}{2(n+8)}]\ensuremath{\epsilon}$. When $n\ensuremath{\rightarrow}\ensuremath{\infty}$ these expansions agree with exact spherical-model results. For n=3n=3n=3 and d=3d=3d=3 series expansions indicate $\ensuremath{\varphi}\ensuremath{\simeq}1.2$ (compared with $\ensuremath{\gamma}\ensuremath{\simeq}1.38$).
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