The critical line of an asymmetric eight vertex model

Mauro Melchiades Doria, R. Shankar

Paul Zinn-Justin

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

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.

Vladimir V. Bazhanov, Vladimir V. Mangazeev

I. M. Nolden

Leo P. Kadanoff

Lines of critical points which emerge from the two-dimensional planar model's multicritical point are analyzed. These lines seem to be in the same universality class as both the Ashkin-Teller and the eight-vertex (8V) models' critical lines, with the multicritical point being isomorphic with the 8V model at both the points $tanh2\ensuremath{\lambda}=\frac{\sqrt{2}}{2} \mathrm{and} \ensuremath{-}1$. Expansions of critical indices about these values of $\ensuremath{\lambda}$ are performed. If this analysis is right, then this work permits the evaluation of a whole class of interesting correlation functions at the critical point of the $F$ model and that of the four-state Potts model.