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Journal of Physics A Mathematical and General

On the phase diagram of the chiral Potts model

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

Published Jul 7, 1989• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/22/13/048

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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.
A Monte Carlo renormalization-group scheme based on a ``floating sublattice'' blocking rule is constructed for the two-dimensional three-state chiral clock model. The presence of a critical phase is established by matching certain wave-vector-dependent correlation functions derived from lattices differing in linear size by a factor of 2. The wave vector, which in a function of temperature and the asymmetry parameter \ensuremath{\Delta}, is determined from the simulations. For \ensuremath{\Delta}=0.45, a critical phase is established in a temperature range. For \ensuremath{\Delta}=0.35, no critical phase is observed, suggesting that the phase diagram has a Lifschitz point in the interval 0.35<\ensuremath{\Delta}<0.45. Alternatively, the wave vector and the width of the critical phase at \ensuremath{\Delta}=0.35 are much smaller than for \ensuremath{\Delta}=0.45..AE
Three-state Potts ferromagnets on the simple cubic lattice in random fields are studied by extensive Monte Carlo simulation. The implications of the possible hyperscaling violation to finite-size scaling are discussed. Evidence for a second-order transition is obtained, as well as rough estimates for critical exponents. A qualitative phase diagram is proposed compatible with the predictions of Blankschtein et al. on the random field-induced shift of the tricritical curve q = q c ( d ) in the plane of variables dimensionality d and number of states q .
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 (qs{\mathit{q}}_{\mathit{s}}qs​,qt{\mathit{q}}_{\mathit{t}}qt​) 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 study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, K between neighboring triangular sites, and J between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer-matrix calculations and Monte Carlo simulations. Our investigation covers the whole (K,J) phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case K<0, where the model is geometrically frustrated. In particular, we find that there are, for all finite J, two transitions when K is varied. Their critical properties are explored. In the limits J→±∞ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.