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Physical Review Letters

Exact Solution of an Ising Model with Three-Spin Interactions on a Triangular Lattice

R. J. Baxter, Fa Yueh Wu

Published Nov 19, 1973• 318 citations
Publisher

Abstract

The Ising model on a triangular lattice with three-spin interactions is solved exactly. The solution, which is obtained by solving an equivalent coloring problem using the Bethe Ansatz method, is given in terms of a simple algebraic relation. The specific heat is found to diverge with indices $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\frac{2}{3}$.

DOI
10.1103/physrevlett.31.1294

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Journal of Physics A Mathematical Nuclear and General•May 1, 1974•18 citations
The Ising model on a triangular lattice with three-spin interactions is solved exactly. The solution, which is obtained by solving an equivalent coloring problem using the Bethe Ansatz method, is given in terms of a simple algebraic relation. The specific heat is found to diverge with indices \ensuremathα=\ensuremathα\ensuremath′=23\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\frac{2}{3}\ensuremathα=\ensuremathα\ensuremath′=32​.
The one-dimensional Ising model is investigated by generalizing the Bethe approximation, which, in this case, gives exact solutions. The energy, specific heat and the zero field susceptibility for S =1, 3/2 and 2 except the susceptibility for S =2 are calculated exactly and compared with the results of Suzuki et al. . As a direct application of this method, the special lattice called the Bethe lattice is treated, and the Curie temperature of the lattice for S =1 is obtained. This method is also applied to solve the one-dimensional Ising model with the second neighbor interactions as well as the first neighbor ones, and the energy and specific heat for S =1/2 are calculated.