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Non-universal critical behaviour of the two-dimensional Ising model with crossing bonds

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  • Minami, Kazuhiko
  • Suzuki, Masuo

Abstract

The two-dimensional square lattice Ising model with the nearest-neighbour ferromagnetic interaction J and the next-nearest-neighbour antiferromagnetic interaction J' is investigated in the interaction range |J/J'| ⩽ 0.8. This model is shown to violate the ordinary universality hypothesis. Estimations of critical temperature as a function of J/J' by means of an extrapolation method results in the exact critical temperature T∗c when |J/J'| = 0 and in an approximate Tc accurate up to the fourth digit when |J/J'| is small. The critical exponent γ is estimated as a function of |J/J'| with the use of the multi-effective-field theory and the coherent-anomaly method. It is shown, consequently, that γ varies continuously as |J/J'| increases.

Suggested Citation

  • Minami, Kazuhiko & Suzuki, Masuo, 1993. "Non-universal critical behaviour of the two-dimensional Ising model with crossing bonds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(1), pages 152-166.
    • Handle: RePEc:eee:phsmap:v:192:y:1993:i:1:p:152-166
    DOI: 10.1016/0378-4371(93)90149-X
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    References listed on IDEAS

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    1. Morita, Hiroshi & Ishii, Hiroaki, 1992. "A stochastic improvement method for stochastic programming," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 477-487, November.
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    Cited by:

    1. Moodie, Jordan C. & Kainth, Manjinder & Robson, Matthew R. & Long, M.W., 2020. "Transition temperature scaling in weakly coupled two-dimensional Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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