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

Proceedings of the Royal Society of London A Mathematical and Physical Sciences

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

G S Joyce

Published Apr 22, 1975• 14 citations
Publisher

Abstract

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
DOI
10.1098/rspa.1975.0051

Related papers

Low-temperature expansions for the Ising model with pure triplet interactions on the triangular lattice

M F Sykes, M G Watts, J. L. Martin

Recently published series expansions of Griffiths and Wood (1973) for the Ising model with pure triplet interactions on the triangular lattice are found to be inconsistent with the exact solution of Baxter and Wu (1973). The necessary corrections are given.

Journal of Physics C Solid State Physics•Dec 11, 1973•3 citations

Critical indices for an Ising model with pure triplet interactions on the triangular lattice

M G Watts

Extended series for the spontaneous magnetization and reduced susceptibility of the triplet model on the triangular lattice are analysed using Pade approximants. Baxter and Wu's exact solution (1973) for the specific heat has been used as a guide in interpreting the approximants and it is concluded that beta =0.080+or-0.005 and gamma '=1.5+or-0.15.

Journal of Physics A Mathematical Nuclear and General•May 1, 1974•18 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

Triplet order parameters in triangular and honeycomb Ising models

Ian Graham Enting

It is shown that the ratios of certain triplet order parameters to magnetisation in honeycomb and diamond lattice Ising models can be easily calculated. Applying the star-triangle transformation reproduces the result obtained by Baxter (see ibid., vol.8, p.1797 (1975)) on the triangular lattice. The new derivation indicates that exact solutions for triplet order parameters are of only limited use as checks on series expansions.

Journal of Physics A Mathematical and General•Oct 1, 1977•22 citations

Exact solution of Z(N) invariant spin models on a triangular lattice

Roberto Nicolau Onody, V. Kurak

Based on Baxter's ideas the authors present a method to solve spin models on triangular lattices. If the model has only nearest neighbour interaction and it satisfies the star-triangle relation then the exact free energy can be obtained. They apply the method to reobtain the critical triangular Potts model and to extend the self-dual Z(N) solutions of Fateev and Zamolodchikov to the triangular lattice.

Journal of Physics A Mathematical and General•Aug 1, 1984•4 citations

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

R. J. Baxter

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

Australian Journal of Physics•Jun 1, 1974•52 citations