Phase diagram of the square-lattice three-state Potts antiferromagnet with a staggered polarization field

We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising-type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.     

Phase transitions in three-dimensional three-state Potts model

We have performed a Monte Carlo investigation of the nature of the phase transition in the three-state, three-dimensional Potts model with nearest and next nearest neighbour coupling. We find strong evidence for a first-order phase transition in the case of ferromagnetic coupling. In the case of a first neighbour ferromagnetic coupling and second neighbour antiferromagnetic, there is evidence for a second-order transition. This result supports the idea that a second-order transition can be present in systems which, according to the Landau criterium, should only undergo a first-order transition.     

Finite-size scaling of the three-state Potts model on a simple cubic lattice

Finite-size scaling is studied for the three-state Potts model on a simple cubic lattice. We show that the specific heat and the magnetic susceptibility scale accurately as the volume. The correlation length exhibits behaviors expected for a genuine first-order transition; the one extracted from the unsubtracted correlation function shows a characteristic finite-size behavior, whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point.     

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, , with a>0, and observe that this system seems to have critical exponents and which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0 Received 5 April 2000     

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.     

Phase transitions in the three-state antiferromagnetic Potts model for different lattices

The ordered phases in the three-state antiferromagnetic Potts model for different lattices are investigated using the cluster-variation method in the pair approximation. There are two types of low-temperature ordered phases. The intermediate-temperature ordered phases are also analyzed.     

Interfacial tension of the three-state Potts model on a square lattice at a negative fields

We calculate the interfacial tension of the three-state Potts model on a square lattice at a negative field by extending the method of Selke and Pesch, which is used in the model at zero field. The transition temperature and therefore the phase diagram of the model are determined by the vanishing of the interfacial tension.     

Phase separation of the Potts model in the square lattice

When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.     

Phase transitions in the two-dimensional antiferromagnetic Potts model on a triangular lattice

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions (L > 120). No first-order PTs are observed for systems with L < 120.     

Thermodynamic and magnetic properties of a three-state Potts model on a triangular lattice with next-neighbor interactions

Physics of the Solid State - Using Monte Carlo calculations, we study the thermodynamic and magnetic properties of 2D structures that can be described by a three-state Potts model on a triangular...     

Susceptibility amplitude ratio in the two-dimensional three-state Potts model

We analyze Monte Carlo simulation and series-expansion data for the susceptibility of the three-state Potts model in the critical region. The amplitudes of the susceptibility on the high- and the low-temperature sides of the critical point as extracted from the Monte Carlo data are in good agreement with those obtained from the series expansions and their (universal) ratio compares quite well with a recent quantum field theory prediction by Delfino and Cardy.     

Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

Phase transition properties of 3D Potts models

Using multicanonical Metropolis simulations we estimate phase transition properties of 3D Potts models for q=4 to 10: The transition temperatures, latent heats, entropy gaps, normalized entropies at the disordered and ordered endpoints, interfacial tensions, and spinodal endpoints.     

Quantum phase transition of the randomly diluted heisenberg antiferromagnet on a square lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.     

Propagation of order in the dilute antiferromagnetic three-state Potts model

A recent analysis of the propagation of order in a dilute 3-state Potts antiferromagnetic model on a triangular lattice at zero temperature by Adleret al. has shown the importance of nonlocality in the propagation of order. We study a linearized continuous version of this model, which can be mapped onto three independent percolation problems. We discuss the respective roles of nonlocality and nonlinearity, in particular in connection with central-force percolation.     

The magnetic critical exponent in the three-state three-dimensional Potts model

We perform a numerical study of the Potts model q=3 in three dimensions with nearest neighbour and next to nearest neighbour couplings by means of the finite-size renormalization group method. The analysis of the magnetic critical exponents is complementary to the one of the thermal critical exponent already presented by us and confirms our conclusions that the transition from the disordered phase to the low-temperature ordered phase is first order.     

Critical behavior of three-state Potts model on decagonal covering quasilattice

The three-state Potts model on a 2D decagonal covering quasilattice is investigated by means of the Monte Carlo simulation. The periodic boundary conditions are realized on a rhombus-like covering pattern. By use of the finite-size scaling analysis, we obtain the critical temperature and the critical exponents. The critical temperature is higher than that of the square lattice mainly due to the larger mean coordination number of the covering model. The critical exponents are close to the corresponding values of the 2D periodic lattices, which means that the Potts model on the covering structure may belong to the same universal class as that of the periodic lattices.