Phase transition in the 3-state Potts antiferromagnet on the diced lattice

Abstract

We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically-driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v = e^J - 1 = -0.860599 +- 0.000004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.

4 pages, LaTeX2e/revtex4, includes 4 figures. Version 3 (published in PRL) contains several small improvements in response to referees' comments

Cited by in corpus (10)

• Uniform tiling with electrical resistors
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• Partial long-range order in antiferromagnetic Potts models
• Ising antiferromagnet on the 2-uniform lattices
• Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in three-state Potts antiferromagnetic thin film
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Degeneracy and ordering of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
• Critical manifold of the Potts model: Exact results and homogeneity approximation
• Characterizing spin ordering via maximal row correlation in classical spin models