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Physical review. B, Condensed matter

Universality for the critical lines of the eight-vertex, Ashkin-Teller, and Gaussian models

Adrianus M. M. Pruisken, A. C. Brown

Published Feb 1, 1981• 21 citations
Publisher

Abstract

A perturbation expansion has been performed for the critical lines of the eight-vertex and Ashkin-Teller models around the decoupling point. The critical temperature and the details of the mapping of these lines onto the Gaussian-model critical line is calculated to second order in the marginal parameters. We find agreement with the exactly known results for these models and with the mapping formalism of Kadanoff and Brown.

DOI
10.1103/physrevb.23.1459

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The universal critical point ratio of the square of the second moment of the order parameter to its fourth moment, denoted as Q, is exploited to determine the position of the critical Ising transition lines in the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the Q ratio in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data for the L x L squaxe clusters with L <= 9. The same method is used to determine the critical Ising transition line on the phase diagram of the Blume-Capel (BC) model (L <= 11). We have also calculated the Q ratio for the q=3 Potts model in the critical point. The previously predicted scaling relation for this universality class is confirmed by our results for L <= 12.