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Criticality of two- and three-spin Ising model in an external field on a fractal family

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  • Redinz, JoséArnaldo
  • de Magalhães, AglaéCristina Navarro

Abstract

We study the Ising model with pair and alternate triplet interactions subjected to an external magnetic field on a family of infinitely ramified fractal lattices with a triangular topology. The three-dimensional phase diagram and correlation length critical exponents are calculated within an exact real-space renormalization group framework. The zero-field results for the ferromagnetic model show that, although the pure triplet case and the pure nearest-neighbor pair interaction model are in different universality classes, there is no crossover phenomenon since the system becomes paramagnetic in the mixed case. In the pure nearest-neighbor antiferromagnetic model, the appearance of an unusual Berker and Kadanoff's-phase type (with a power-law decay of correlations) when the fractal dimension is sufficiently high is destroyed by the application of a magnetic field or a triplet interaction field.

Suggested Citation

  • Redinz, JoséArnaldo & de Magalhães, AglaéCristina Navarro, 1997. "Criticality of two- and three-spin Ising model in an external field on a fractal family," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 27-44.
    • Handle: RePEc:eee:phsmap:v:246:y:1997:i:1:p:27-44
    DOI: 10.1016/S0378-4371(97)00361-0
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    References listed on IDEAS

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    1. Saul Blumenthal & J. Arthur Greenwood & Leon H. Herbach, 1984. "Series Systems and Reliability Demonstration Tests," Operations Research, INFORMS, vol. 32(3), pages 641-648, June.
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