Journal of Physics A Mathematical Nuclear and General

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

M G Watts

Published May 1, 1974• 18 citations

Abstract

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.

DOI: 10.1088/0305-4470/7/7/001

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 PhysicsDec 11, 19733 citations

The critical exponents of Ising model systems with pure three-body interactions. III

David W. Wood, H P Griffiths

For pt. II, see abstr. A64455 of 1973. The critical-point exponents of two Ising models with pure three-spin coupling terms are examined using low-temperature (T<T c ) series expansions for the thermodynamic functions. In particular the critical isotherm exponent delta is examined by applying numerical extrapolation methods to the critical isotherm. The two models are (a) a two-dimensional triangular lattice and (b) a three-dimensional face-centred cubic lattice. Direct numerical estimates of alpha ', beta and delta for (b) show that the scaling relations hold for this model and it is found that alpha '=0.655, beta =0.0538, gamma =1.24, nu =0.448, eta =-0.76, and delta =24 on the basis of the scaling relations. The numerical accuracy of the exponents beta and delta for model (a) does not permit an independent verification of the scaling relations; assuming scaling to hold here also, and using the exact result alpha '= 2 / 3 obtained by Baxter and Wu, it is found that gamma '=1.187+or-0.006, nu = 2 / 3 , eta =0.219+or-0.009, beta =0.073+or-0.003, and delta =17.3+or-0.8.

Journal of Physics C Solid State PhysicsApr 21, 197419 citations

Determination of critical behaviour from series expansions in lattice statistics. IV

Anthony John Guttmann, Colin J. Thompson, Barry William Ninham

For pt. III, see abstr. A21890 of 1970. A new low-temperature expansion variable for the Ising model is given. Expansions in the new variable, x=1-tanh(J/kT), then converge right up to the critical point. Power series in the new variable are derived, and then analysed by the Pade method and the method of N-point fits. For the spontaneous magnetization of the Ising model in three dimensions. beta =0.312+or-0.002 for the simple cubic lattice, beta =0.3125+or-0.0015 for the body-centred cubic lattice, and beta =0.312+or-0.004 for the face-centred cubic lattice. For the low-temperature susceptibility gamma =1.30+or-0.02, gamma =1.28+or-0.04, and gamma '=1.29+or-0.04 for the simple cubic, body-centred cubic and face-centred cubic lattices respectively. For the low-temperature specific heat the authors estimate 1 / 16 <or= alpha =0.2 for all three lattices.

Journal of Physics C Solid State PhysicsAug 1, 197014 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 SciencesApr 22, 197514 citations

Low-Temperature Behavior of Antiferromagnetic Ising Model on Triangular Lattice

Tsuyoshi Horiguchi, Kazuyuki Tanaka, Tohru Morita

We derive low-temperature expansions of the internal energy, the specific heat and so on for the antiferromagnetic Ising model on a triangular lattice by using the expression obtained by Stephenson. We propose to use Δ T = exp(-2β J ) as the reduced temperature variable near the critical temperature. We then conclude the values of the critical exponents α, ν, γ, δ and Δ as α=0, ν=1, γ=3/2, δ=7 and Δ=7/4.

Journal of the Physical Society of JapanJan 15, 199212 citations

The critical index of the magnetic susceptibility of 3D Ising models

Peter R. Graves-Morris

Series expansions for certain thermodynamic variables have been computed for various standard model lattices. The high-temperature series for the magnetic susceptibility of the Ising model of three-dimensional SC, BCC and FCC lattices allows estimates of the critical index gamma of each series to be made. Dramatic progress in this direction was made by the Pade Dlog method, and here a similar technique is introduced. Estimates of gamma from row sequences of generalised inverse vector-valued Pade approximants are made. The results point to the conclusion that gamma =1.2406+or-0.0017 is the critical index common to all three lattices.

Journal of Physics A Mathematical and GeneralApr 21, 19883 citations