Sublattice renormalization transformations for spin 12 models on a square lattice

B. Nienhuis, Aa.S. Sudbø and E.H. Hauge

Physica A: Statistical Mechanics and its Applications, 1978, vol. 92, issue 1, 222-232

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.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:92:y:1978:i:1:p:222-232

DOI: 10.1016/0378-4371(78)90030-4

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