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Planar spin glasses on d-dimensional hierarchical lattices: a Migdal-Kadanoff renormalization-group analysis

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  • Nobre, F.D.
  • Mariz, A.M.
  • Sousa, E.S.

Abstract

The p-state clock spin glass is studied on d-dimensional hierarchical lattices by means of a Migdal-Kadanoff renormalization-group approach. Considering such procedure as an approximation for Bravais lattices, the spin-glass critical temperature is computed for several values of p as a function of the dimension. Our main results are: (a) the XY limit (p → ∞) presents a small, but finite, critical temperature in three dimensions; (b) the Ising and XY spin glasses exhibit the same lower critical dimensions (dℓ ≈ 2.46, in our case) as predicted by early arguments.

Suggested Citation

  • Nobre, F.D. & Mariz, A.M. & Sousa, E.S., 1993. "Planar spin glasses on d-dimensional hierarchical lattices: a Migdal-Kadanoff renormalization-group analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 196(4), pages 505-518.
    • Handle: RePEc:eee:phsmap:v:196:y:1993:i:4:p:505-518
    DOI: 10.1016/0378-4371(93)90032-Y
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