Rotationally symmetric ordered phase in the three-state antiferromagnetic Potts model (original) (raw)
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Low-temperature phase of the three-state antiferromagnetic Potts model on the simple-cubic lattice
Physical Review E, 1996
The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free energy difference between the broken-sublattice-symmetry and the permutationally-symmetric-sublattices phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.
Journal of Physics A: Mathematical and General, 2006
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions; one belongs to the ferromagnetic three-state Potts universality class, and the other to the Ising universality class. The phase diagram obtained is quantitatively consistent with the transfer matrix calculation. The Ising transition in the large nearest-neighbor interaction limit has been made clear by the detailed analysis of the energy density of states.
Three-dimensional antiferromagneticq-state Potts models: application of the Wang-Landau algorithm
Journal of Physics A: Mathematical and General, 2001
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with q=3, 4, 5 and 6. We obtain the finitetemperature phase transition for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For q=6 there exists no order for all the temperatures. We also study the ground-state properties. The size-dependence of the ground-state entropy is investigated. We find that the ground-state entropy is larger than the contribution from the typical configurations of the brokensublattice-symmetry state for q = 3. The same situations are found for q = 4, 5 and 6.
arXiv: Statistical Mechanics, 2018
This study present a Monte Carlo investigations of low-temperature magnetic ordering and phase transitions in three-state Potts model on triangular lattice with various exchange interactions between nearest (J1) and next-nearest (J2) neighbors. The density of states for varying J1 and J2 are calculated. The magnetic structure of the ground state for various J1 and J2 are obtained. The critical temperature are calculated and the order of the phase transition determined. The density of states difference (DOSD) and histogram analysis method are used to investigate the order of the phase transitions. The frustrated regions are determined. It is shown, that for negative J1 the high degeneration of the ground state are in fully frustrated area -1<=J2/abs(J1)<=-0.2. For positive J1 frustration are occurred in area -1<=J2/J1<=-0.5, but only in point J2/J1=-1 the system have a high degeneration and are fully frustrated. The phase diagram of the three-state triangular Potts model ...
The 3State Square-Lattice Potts Antiferromagnet at Zero Temperature
1998
We study the 3-state square-lattice Potts antiferromagnet at zero temperature by a Monte Carlo simulation using the Wang-Swendsen-Kotecký cluster algorithm, on lattices up to 1024 × 1024. We confirm the critical exponents predicted by Burton and Henley based on the height representation of this model.
Partial order and finite-temperature phase transitions in Potts models on irregular lattices
We have evaluated the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union-Jack lattice using tensor-based numerical methods. We demonstrate that this model exhibits a previously unknown, ``entropy-driven,'' finite-temperature phase transition to a partially ordered state. By considering also the 3-state Potts model on the diced lattice, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.
Phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
Physical Review E
In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisectedhexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using highprecision Monte Carlo simulations and two complementary analysis methods, we conclude that there is a finite-temperature first-order transition point. This one separates a paramagnetic hightemperature phase, and a low-temperature phase where five phases coexist. This phase transition is very weak in the sense that its latent heat (per edge) is two orders of magnitude smaller than that of other well-known weak first-order phase transitions.
Phases of the three-state Potts model in three spatial dimensions
Arxiv preprint hep-lat/9305010, 1993
The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to 128 3 volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered phases. In both phases clusters of like spins are observed with irregular boundaries. In the ordered phase the two different non-favored spins are found to attract each other with a long but finite range. As a result, the neighborhoods of the non-favored spins are interpreted as domains of the disordered phase. This explains why the first-order phase transitions associated with the global Z 3 symmetry, including the SU(3) pure-gauge one, are so weak.
Physical Review Letters, 2004
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.