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Journal of Physics C Solid State Physics

Two phase transitions in triplet Ising models

Fa Yueh Wu

Published Jan 28, 1977• 9 citations
Publisher

Abstract

It is shown that the three-spin Ising model on a triangulated dice lattice is equivalent to an Ashkin-Teller model. It is concluded from the expected critical behaviour of the Ashkin-Teller model that the triplet model exhibits two phase transitions. Generalization of the consideration to other lattices and a suggestion on the possible order parameters associated with the transitions are given.

DOI
10.1088/0022-3719/10/2/001

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It is shown that the three-spin Ising model on a triangulated dice lattice is equivalent to an Ashkin-Teller model. It is concluded from the expected critical behaviour of the Ashkin-Teller model that the triplet model exhibits two phase transitions. Generalization of the consideration to other lattices and a suggestion on the possible order parameters associated with the transitions are given.
The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s ) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈 s 〉=〈α s 〉=0) and the correlated ordered (〈 s 〉 ≠0 and 〈α〉=〈 s 〉=0) states.