Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Australian Journal of Physics

Ising Model on a Triangular Lattice with Three-spin Interactions. I. Free Energy and Correlation Length

R. J. Baxter

Published Jun 1, 1974• 52 citations
Publisher

Abstract

Following the demonstration in Part I that the Ising mogel with three-spin interactions on a triangular lattice is equivalent to a colouring problem on a hexagonal lattice, and that a generalized Bethe ansatz can be used to obtain equations for the eigenv
DOI
10.1071/ph740369

Related papers

Ising Model on a Triangular Lattice with Three-spin Interactions. I. The Eigenvalue Equation

R. J. Baxter, Fa Yueh Wu

It is shown that the Ising model with three-spin interactions on a triangular lattice is equivalent to a site-colouring problem on a hexagonal lattice. The transfer matrix method is then used to solve the colouring problem. The colouring of two neighbouri

Australian Journal of Physics•Jun 1, 1974•129 citations

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

R. J. Baxter, Fa Yueh Wu

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 $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\frac{2}{3}$.

Physical Review Letters•Nov 19, 1973•318 citations

Analytic properties of the Ising model with triplet interactions on the triangular lattice

G S Joyce

Abstract The analytic properties of the Baxter-W u solution for the Ising model with pure triplet interactions on the triangular lattice are investigated. In particular, it is shown that the free energy per spin of the model can be written in the explicit form

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Apr 22, 1975•14 citations

A free-fermion model, and the solution of an Ising model with pure triplet interactions

David W. Wood

A vertex model problem on the honeycomb lattice is reduced to an eight-vertex model problem which satisfies the free-fermion condition. An Ising model in which only triplet coupling terms are present on a decorated version of the triangular lattice is equivalent to this free-fermion model, thus providing an example of a pure three-spin interaction which has the conventional Ising-like logarithmic singularity in the specific heat, independently of the values of the coupling constants.

Journal of Physics C Solid State Physics•Mar 28, 1973•7 citations

Local three-spin correlations in the free-fermion and planar Ising models

R. J. Baxter, T. C. Choy

Abstract A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jun 8, 1989•21 citations

Bethe ansatz solution of triangular trimers on the triangular lattice

Alain Verberkmoes, Bernard Nienhuis

Recently, a model consisting of triangular trimers covering the triangular lattice was introduced and its exact free energy given. In this paper we present the complete calculation leading to this exact result. The solution involves a coordinate Bethe ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model by Widom and Kalugin. The connection of the trimer model with related solvable models is discussed.

arXiv:cond-mat/9909068•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•May 24, 2001•11 citations