The authors study the phase diagram of the isotropic three-state chiral Potts model. Monte Carlo simulations performed on twisted square lattices with different sizes up to 64*64 indicate different types of critical curves. In particular, a floating phase seems to occur. Finite-size scaling analyses are performed at some specific critical points. The phase diagram they propose is discussed using exact results.

Journal of Physics A Mathematical and GeneralJul 7, 19897 citations

Physica A Statistical Mechanics and its Applications

Phase diagram of a six-state chiral Potts model

H. Meyer, J C Anglès d'Auriac, J.-M. Maillard, G. Rollet

Published Aug 1, 1994• 17 citations

Publisher

DOI: 10.1016/0378-4371(94)90056-6

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We present the two-dimensional phase diagram of an isotropic six-state chiral Potts model with a noncyclic Boltzmann weight matrix. This model has been introduced as being preintegrable in the sense that a very constraining functional relation for the partition function is known. The phase diagram shows itself to be very rich. In one region the model almost decouples, like a ( ${\mathit{q}}_{\mathit{s}}$ , ${\mathit{q}}_{\mathit{t}}$ ) model, in a product of two simpler models; while in another region a mean-field calculation gives good results compared to our Monte Carlo simulations. All the transition lines, as well as their order, are numerically determined. Besides, using the above-mentioned functional relation, an exact form for one of these transition lines is proposed. The low-energy states are also analyzed showing a variety of zero-temperature behavior in the different regions of the phase diagram.We present the two-dimensional phase diagram of an isotropic six-state chiral Potts model with a noncyclic Boltzmann weight matrix. This model has been introduced as being preintegrable in the sense that a very constraining functional relation for the partition function is known. The phase diagram shows itself to be very rich. In one region the model almost decouples, like a (${\mathit{q}}_{\mathit{s}}$,${\mathit{q}}_{\mathit{t}}$) model, in a product of two simpler models; while in another region a mean-field calculation gives good results compared to our Monte Carlo simulations. All the transition lines, as well as their order, are numerically determined. Besides, using the above-mentioned functional relation, an exact form for one of these transition lines is proposed. The low-energy states are also analyzed showing a variety of zero-temperature behavior in the different regions of the phase diagram.

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On the phase diagram of the chiral Potts model

J C Anglès d'Auriac, David Hansel, J.-M. Maillard

Journal of Physics A Mathematical and GeneralJul 7, 19897 citations

{\mathit{q}}_{\mathit{s}}

{\mathit{q}}_{\mathit{t}}

) model, in a product of two simpler models; while in another region a mean-field calculation gives good results compared to our Monte Carlo simulations. All the transition lines, as well as their order, are numerically determined. Besides, using the above-mentioned functional relation, an exact form for one of these transition lines is proposed. The low-energy states are also analyzed showing a variety of zero-temperature behavior in the different regions of the phase diagram.