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Journal of Physics A Mathematical and General

Critical behaviour of a (1+1) dimensional Potts model with ferromagnetic and antiferromagnetic interactions

Hans Jürgen Herrmann, H. O. Mártin

Published Feb 21, 1984• 14 citations
Publisher

Abstract

The authors study the one-dimensional quantum Hamiltonian version of a two-dimensional three-state Potts model on a square lattice which has ferromagnetic interactions in the x direction and antiferromagnetic interactions in the y direction in the limit of strong coupling in the x direction. They find a massless low-temperature behaviour. The transition point which has an essential singularity is located at a different point as previously conjectured.

DOI
10.1088/0305-4470/17/3/027

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Physical review. B, Condensed matter•Feb 1, 1982•4 citations
The authors study the one-dimensional quantum Hamiltonian version of a two-dimensional three-state Potts model on a square lattice which has ferromagnetic interactions in the x direction and antiferromagnetic interactions in the y direction in the limit of strong coupling in the x direction. They find a massless low-temperature behaviour. The transition point which has an essential singularity is located at a different point as previously conjectured.
A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.
A previously proposed renormalization-group realization is applied to the qqq-state Potts model for any qqq in (1 + 1)- and (2 + 1)-dimensional lattices of different coordination number. Ferromagnetic and antiferromagnetic critical points are found and the corresponding exponents are computed in a very simple way.