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Analysis of the Migdal transformation for models with planar spins on a two-dimensional lattice

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  • Sokalski, K.
  • Ruijgrok, Th.W.
  • Schoenmaker, B.

Abstract

By numerical and analytical investigations we show that the bond-moving transformation of Migdal for planar spins on a two-dimensional lattice possesses a very rich structure. We find an infinite hierarchy of one-, three- and higher-dimensional fixed spaces. In addition to phase transitions of the Kosterlitz-Thouless-type, we find Ising-like transitions, for which the critical exponents are the same as those of the q-state Potts model in the Migdal approximation. These critical exponents are constant within each fixed space. The phase diagram is constructed for two specially chosen potentials.

Suggested Citation

  • Sokalski, K. & Ruijgrok, Th.W. & Schoenmaker, B., 1987. "Analysis of the Migdal transformation for models with planar spins on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 322-352.
    • Handle: RePEc:eee:phsmap:v:144:y:1987:i:2:p:322-352
    DOI: 10.1016/0378-4371(87)90195-6
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