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Transition temperature scaling in weakly coupled two-dimensional Ising models

Author

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  • Moodie, Jordan C.
  • Kainth, Manjinder
  • Robson, Matthew R.
  • Long, M.W.

Abstract

We investigate the proposal that for weakly coupled two-dimensional magnets the transition temperature scales with a critical exponent which is equivalent to that of the susceptibility in the underlying two-dimensional model, γ. Employing the exact diagonalization of transfer matrices we can determine the critical temperature for Ising models accurately and then fit to approximate this critical exponent. We find an additional logarithm is required to predict the transition temperature, stemming from the fact that the heat capacity exponent α tends to zero for this Ising model, complicating the elementary prediction. We suggest that the excitations of the transfer matrix correspond to thermalized topological excitations of the model and find that even the simplest model exhibits significant changes of behavior for the most relevant of these excitations as the temperature is varied.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318369
    DOI: 10.1016/j.physa.2019.123276
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    References listed on IDEAS

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    1. Monroe, James L, 2004. "The bilayer Ising model and a generalized Husimi tree approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 563-576.
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    3. B. Mirza & T. Mardani, 2003. "Phenomenological renormalization group approach to the anisotropic two-layer Ising model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(3), pages 321-324, August.
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    5. Angelini, L. & Caroppo, D. & Pellicoro, M. & Villani, M., 1995. "The two-layer Ising film correlation length and critical curve by CLE and CVM methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 447-466.
    6. 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.
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