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arXiv:cond-mat/9705292 · Physics Letters B

Coupled critical models: application to Ising-Potts models

Pascal Simon

Published Sep 1, 1997• 3 citations
arXivHTMLPDF
DOI
10.1016/s0370-2693(97)00787-9

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The exact solution of a general Z(4) gauge Potts model with a single and double plaquette representation of the action is found on a subspace of gauge-coupling parameters on the square and triangular lattices. The two Ising-type critical lines of a second-order phase transition for the model on a square lattice are found. For the model on a triangular lattice the two critical surfaces of an Ising-type and two nontrivial lines of a second-order phase transition with different critical behavior than on the critical surfaces are found. It is shown that a two-dimensional (2D) general Z(4) gauge Potts model with single and double plaquette representation of the action and a 2D spin-3 / 2 Ising model belong to the same universality class.
The Legendre transformation, a modification of the decimation method used in the real space renormalisation group, is employed to study the critical behaviour of the two-dimensional S-state Potts model which exhibits a second-order phase transition for S<or=4. Thermal and magnetic critical exponents are calculated for the percolation (S to 1), Ising (S=2) and three- and four-state Potts models. Decimation estimates of the critical exponents and critical points for S=2, 3 and 4 are also presented.
Strong and weak coupling series expansions are used to investigate the critical properties of the S=1 multispin coupling Ising chain in the presence of a transverse field. The order of the transition goes from second order to first order when more than three spins are coupled. According to the numerical results the two-spin and three-spin coupling models belong to the Ising and the four-state Potts universality classes, respectively. Thus the critical properties of the model do not depend on the value of the spin, even when three spins are coupled.