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arXiv:cond-mat/0208387 · Physical review. B, Condensed matter

Monte Carlo study of an extended three-state Potts model on the triangular lattice

Z. F. Wang, B. W. Southern, David A. Lavis

Published Feb 27, 2003• 7 citations
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Abstract

By introducing a chiral term into the Hamiltonian of the three-state Potts model on a triangular lattice additional symmetries are achieved between the clockwise and anticlockwise antiferromagnetic states and the ferromagnetic state. This model is investigated using Monte Carlo methods. We investigate the full phase diagram and find evidence for a line of tricritical points separating the ferromagnetic and antiferromagnetic phases.

DOI
10.1103/physrevb.67.054415

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By introducing a chiral term into the Hamiltonian of the three-state Potts model on a triangular lattice additional symmetries are achieved between the clockwise and anticlockwise antiferromagnetic states and the ferromagnetic state. This model is investigated using Monte Carlo methods. We investigate the full phase diagram and find evidence for a line of tricritical points separating the ferromagnetic and antiferromagnetic phases.
We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagom\'e lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.
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.
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.
We study the phase diagram of the three-state Potts model on a triangular lattice with general interactions (ferro- and/or antiferromagnetic) between nearest-neighbor spins. When the interactions along two lattice-vector directions are antiferromagnetic and infinitely strong, this model becomes equivalent to a six-vertex model and exhibits a first-order potassium dihydrogen phosphate (KDP) transition from an ordered phase into a critical phase. Comparing the excitations that occurred by relaxing the restriction of infinite-strength interactions and those in the eight-vertex model, we analytically obtain the critical index for those excitations and demonstrate the existence of a critical phase for the case of finite antiferromagnetic interactions in two directions and ferromagnetic interactions in the other direction. When the interactions are antiferromagnetic in all three directions, Monte Carlo simulations show that a first-order line emerges from the KDP point and separates completely an ordered phase and a disordered phase. Along the special line where all three antiferromagnetic interactions have the same strength, the cell-spin analysis reveals that the symmetry of the ground states is dual to the symmetry of the n=3 ferromagnetic cubic model which is known to exhibit a first-order phase transition.
The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.