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Journal of Physics A Mathematical and General

High-temperature series expansions for the (2+1)-dimensional Ising model

Haihua He, Chris J. Hamer, J. Oitmaa

Published May 21, 1990• 110 citations
Publisher

Abstract

Using efficient cluster expansion methods, the known high-temperature series for the vacuum energy, specific heat, susceptibility and mass gap of the (2+1)-dimensional Ising model on the square and triangular lattices have been extended by several terms. Estimates of the critical indices demonstrate very convincing universality with the Euclidean version of the model.

DOI
10.1088/0305-4470/23/10/018

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High-temperature series expansions for mixed spin-S-spin-S' Ising models

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Describes the development of high-temperature series expansions for general mixed spin-S-spin-S' Ising models on simple loose-packed lattices. It extends previous work on the simpler special case S'=1/2. Coefficients of the series for the initial susceptibility and specific heat of these models on the square, SC and BCC lattices are presented. A preliminary analysis of the results for the particular case S=1, S'=3/2 is given, and the critical ratio K c and the susceptibility exponent gamma are estimated.

Journal of Physics A Mathematical and General•Oct 21, 1990•25 citations
Using efficient cluster expansion methods, the known high-temperature series for the vacuum energy, specific heat, susceptibility and mass gap of the (2+1)-dimensional Ising model on the square and triangular lattices have been extended by several terms. Estimates of the critical indices demonstrate very convincing universality with the Euclidean version of the model.
Extended series expansions for the high temperature zero-field susceptibility of the Ising model are given in powers of the usual high temperature counting variable v=tanh K; for the triangular lattice to v 16 , for the square lattice to v 21 and for the honeycomb lattice to v 32 , inclusive. The asymptotic behaviour of the ferromagnetic and antiferromagnetic susceptibility is studied. It is concluded that the ferromagnetic singularity is not exactly factorizible. The antiferromagnetic susceptibility of the square and honeycomb lattices has a singularity of the same type as the energy at the antiferromagnetic critical temperature.
For pt. I see ibid., vol. 5, no. 5, 624. Extended series expansions for the high temperature zero-field susceptibility of the Ising model are given in powers of the usual high temperature counting variable v=tanh K for the simple cubic lattice to v 17 , the body-centred cubic lattice to v 15 , and the face-centred cubic lattice to v 12 , inclusive. The coefficients are analysed by the ratio method and it is estimated that, subject to the implicit assumptions thereof, the critical temperatures correspond to v f =0.21813+or-0.00001 (SC), v f =0.15612+or-0.00003 (BCC) and v f =0.10174+or-0.00001 (FCC). The symptotic behaviour of the coefficients is studied in detail; for the loose-packed lattices the decay of the even-odd oscillation in the ratios is found to be consistent with the assumption that the critical index of the high temperature specific heat is very close to 1/8.
Describes the development of high-temperature series expansions for general mixed spin-S-spin-S' Ising models on simple loose-packed lattices. It extends previous work on the simpler special case S'=1/2. Coefficients of the series for the initial susceptibility and specific heat of these models on the square, SC and BCC lattices are presented. A preliminary analysis of the results for the particular case S=1, S'=3/2 is given, and the critical ratio K c and the susceptibility exponent gamma are estimated.