Low-temperature series for the Ising model

作者: C Domb , A J Guttmann

DOI: 10.1088/0022-3719/3/8/003

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摘要: Low-temperature series for the Ising model show a marked lattice dependence and recent analysis by Guttmann (1969) has revealed pattern of spurious singularities which are sensitive to coordination number lattice. The present paper attempts configurational these series. Taking account Cayley tree configurations with proper volume exclusion, it is found that good approximations obtained all in zero magnetic field. form nonzero field also discussed.

参考文章(16)
George A. Baker, David S. Gaunt, Ising-Model Critical Indices below the Critical Temperature Physical Review. ,vol. 155, pp. 545- 552 ,(1967) , 10.1103/PHYSREV.155.545
David S. Gaunt, George A. Baker, Low-Temperature Critical Exponents from High-Temperature Series: The Ising Model Physical Review B. ,vol. 1, pp. 1184- 1210 ,(1970) , 10.1103/PHYSREVB.1.1184
A J Guttmann, Determination of critical behaviour in lattice statistics from series expansions III Journal of Physics C: Solid State Physics. ,vol. 2, pp. 1900- 1907 ,(1969) , 10.1088/0022-3719/2/11/302
C Domb, N W Dalton, Crystal statistics with long-range forces: I. The equivalent neighbour model Proceedings of the Physical Society. ,vol. 89, pp. 859- 871 ,(1966) , 10.1088/0370-1328/89/4/311
C Domb, Self-avoiding walks and the Ising and Heisenberg models Journal of Physics C: Solid State Physics. ,vol. 3, pp. 256- 284 ,(1970) , 10.1088/0022-3719/3/2/009
G. S. Rushbrooke, On the Thermodynamics of the Critical Region for the Ising Problem The Journal of Chemical Physics. ,vol. 39, pp. 842- 843 ,(1963) , 10.1063/1.1734338
M. F. Sykes, J. W. Essam, D. S. Gaunt, Derivation of Low‐Temperature Expansions for the Ising Model of a Ferromagnet and an Antiferromagnet Journal of Mathematical Physics. ,vol. 6, pp. 283- 298 ,(1965) , 10.1063/1.1704279
D S Gaunt, The critical isotherm and critical exponents of the three-dimensional ising ferromagnet Proceedings of the Physical Society. ,vol. 92, pp. 150- 158 ,(1967) , 10.1088/0370-1328/92/1/321
B. J. Hiley, M. F. Sykes, Probability of Initial Ring Closure in the Restricted Random‐Walk Model of a Macromolecule The Journal of Chemical Physics. ,vol. 34, pp. 1531- 1537 ,(1961) , 10.1063/1.1701041
M E Fisher, The theory of equilibrium critical phenomena Reports on Progress in Physics. ,vol. 30, pp. 615- 730 ,(1967) , 10.1088/0034-4885/30/2/306