Journal of Physics A Mathematical and General

Second-order expansion of indices in the generalised Villain model

Albert B. Zisook

Published Jul 1, 1980• 8 citations

Abstract

Critical indices of several operators in the generalised Villain model are calculated to second order along a critical line emerging from the model's multicritical point. Relations between these expansions support the identification suggested between this line and a critical line of the Ashkin-Teller model.

DOI: 10.1088/0305-4470/13/7/026

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Journal of Physics A Mathematical and General

Second-order expansion of indices in the generalised Villain model

Albert B. Zisook

Published Jul 1, 1980• 8 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/13/7/026

Related papers

Connections between the Critical Behavior of the Planar Model and That of the Eight-Vertex Model

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.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.