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arXiv:cond-mat/9611188 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Low-temperature phase of the three-state antiferromagnetic Potts model on the simple-cubic lattice

Alessandro Pelizzola

Published Dec 1, 1996• 9 citations
arXivHTMLPDF

Abstract

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 sublattice 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.

DOI
10.1103/physreve.54.r5885

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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 sublattice 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.
The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using Monte Carlo simulations. The ordering in a medium temperature range below the critical point is investigated in detail. Two different regimes have been observed: the so-called broken sublattice-symmetry phase dominates at sufficiently low temperatures, while the phase just below the critical point is characterized by an effectively continuous order parameter and by a fully restored rotational symmetry. However, the latter phase is not the permutationally sublattice symmetric phase recently predicted by the cluster variation method.
The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.
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 finite-temperature 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 any temperature. 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 broken-sublattice-symmetry state for q = 3. The same situations are found for q = 4, 5 and 6.
Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.
The phase transition of four-state antiferromagnetic Potts model on simple cubic and body-centered-cubic lattice is studied by cluster Monte Carlo simulations of finite systems up to 963{96}^{3}963 lattice sizes. The result indicates that the size 963{96}^{3}963 is still sufficient to extract asymptotic behavior. However, if one assumes that both models are well described by the usual Ginzburg-Landau Hamiltonian, the result is consistent with the prediction of the field-theoretical analysis that the phase transition is first-order one.
Results of Monte Carlo studies of the qqq-state Potts model on a square lattice with antiferromagnetic nearest-neighbor coupling and ferromagnetic next-nearest-neighbor coupling are presented for q> 3q>~3q> 3. The three-state Potts model shows a variety of unusual transitions whereas for q> 4q>~4q> 4, we find two first-order phase transitions separated by a broken sublattice symmetry state.