Two-dimensional Three-state Potts Model Research Articles

A scaling method for asymptotic analysis of power series

A new method is proposed for asymptotic analysis of power series. In the method the author uses the relation that an n-term power series of a singular quantity with critical exponent beta behaves asymptotically like n- beta at the phase transition point. The method is tested on known series with satisfactory results and used to analyse the power series of the two-dimensional three-state Potts model of Enting, in good agreement with den Nijs' conjecture.

Finite-size calculation of the dynamical critical exponent of the three-state Potts model

The dynamical critical exponent z is calculated using the finite size scaling method for the two-dimensional three-state Potts model with nonconserved dynamics. The value of z is found to be between 2.1-2.3, with the most likely value being 2.2.

Critical relaxation of the three-state Potts model

The dynamical exponent z is obtained through a Monte Carlo renormalisation group calculation for the two-dimensional three-state Potts model with nonconserved dynamics. The value of z is found to be z=2.7-or+0.4.

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

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.

Phase transition in a two-dimensional three-state Potts model with the addition of an infinite-range coupling

The authors study the two-dimensional three-state Potts model with nearest-neighbour and infinite-range interaction at different values of the two coupling constants. They analyse the intermediate region between the pure infinite-range interaction and the nearest-neighbour one. They find a first-order phase transition for all values of the coupling constants on the coexistence curve except for the pure nearest-neighbour interaction where Baxter's result holds. A Monte Carlo simulation which supports the theoretical expectation is expounded.

Critical exponents of the three-state potts model

The Fernandez-Pacheco duality invariant renormalization group is applied to the hamiltonian version of the two-dimensional three-state Potts model. The fixed point is located at exactly the self-dual critical point K ∗ = 1. The thermal exponent is calculated to be y T=1.1814. This value is in excellent agreement with the low temperature series expansion result of Zwanzig and Ranshaw ( y T = 1.174) and the strong coupling expansion result of Elitzur, Pearson and Shigemitsu ( y T = 1.190). It also seems to lend strong support to den Nijs' recent conjecture that the exact value should be y T = 6/5.

Phase diagrams and higher-order critical points

A classification scheme is presented for the different entities one might expect to find in phase diagrams of fluid mixtures (or other systems where the phases do not break the symmetry of the Hamiltonian) when critical phenomena are present. These include critical points and critical end points of various sorts, higher-order critical points, and entities coexisting in distinct phases. The classification scheme employs the topological properties of the phase diagram, in a space of field variables (temperature, chemical potentials), in the immediate vicinity of the point in question. A graphical method is given for representing some of the topological information in the phase diagram. The entities obtained using a Landau model with one order parameter are discussed and some preliminary results are presented for the case of two order parameters. A phase diagram for a possible fluid analog of the two-dimensional three-state Potts model is described.