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Physical review. B, Condensed matter

Critical and crossover behavior of the two-dimensional φ4 model on a lattice

Paul D. Beale

Published Dec 1, 1981• 9 citations
Publisher

Abstract

A real-space renormalization-group transformation has been carried out on the classical ${\ensuremath{\varphi}}^{4}$ model on a lattice in two dimensions. The critical line has been found for $0<\ensuremath{\theta}<\ensuremath{\infty}$ where $\ensuremath{\theta}$ is the ratio of the site well depth to the nearest-neighbor harmonic coupling energy. For $\ensuremath{\theta}\ensuremath{\ll}1$ (near the displacive limit) the critical temperature qualitatively agrees with a rigorously derived function for ${T}_{c}(\ensuremath{\theta})$ in that limit. In contrast, a previously published Kadanoff-Migdal transformation on the same model predicts that ${T}_{c}(\ensuremath{\theta})$ is linear in $\ensuremath{\theta}$ for $\ensuremath{\theta}\ensuremath{\ll}1$. A crossover to noncritical Gaussian-like behavior is found at temperature ${T}_{0}(\ensuremath{\theta})>{T}_{c}(\ensuremath{\theta})$ for sufficiently small $\ensuremath{\theta}$.

DOI
10.1103/physrevb.24.6711

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