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Sublattice renormalization transformations for spin 12 models on a square lattice

Author

Listed:
  • Nienhuis, B.
  • Sudbø, AA.S.
  • Hauge, E.H.

Abstract

Ising-like models on a square lattice are studied by real space renormalization transformations in which the cells are confined to sublattices. A general class of transformations is discussed which maps all ground states that are invariant under translation over n lattice constants onto themselves. Numerical results on the simplest non-trivial case of n = 2 are given in the lowest approximation involving 16 spins on a square lattice with periodic boundary conditions. The parameter space includes first and second neighbor couplings, four-spin coupling, magnetic field and three-spin coupling. A rich critical structure including seven different fixed points is found. For the calculation of eigenvalues three additional couplings are included: a second neighbor interaction alternating in sign between the two main sublattices, a staggered field, and a staggered three-spin coupling.

Suggested Citation

  • Nienhuis, B. & Sudbø, AA.S. & Hauge, E.H., 1978. "Sublattice renormalization transformations for spin 12 models on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 222-232.
    • Handle: RePEc:eee:phsmap:v:92:y:1978:i:1:p:222-232
    DOI: 10.1016/0378-4371(78)90030-4
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