Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

Abstract

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length $\xi \sim 5000$; the data are consistent with $\xi (\beta )=A{e}^{2\beta }{\beta }^p(1+a_1{e}^{-\beta }+...)$ as $\beta \to \infty$, with $p\approx 1$. The staggered susceptibility behaves as ${\chi }_{stagg}\sim {\xi }^{5/3}$. For q=4 the model is disordered ($ξ\ltapprox 2$) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.

LaTeX, 67 pages including 19 figures. Discussion of alternative scenario added to Sections 4.2.1 and 7.1

References in corpus (2)

• The 3-State Square-Lattice Potts Antiferromagnet at Zero Temperature
• A constrained Potts antiferromagnet model with an interface representation

Cited by in corpus (29)

• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Spanning forests and the q-state Potts model in the limit q \to 0
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models II. Extended Results for Square-Lattice Chromatic Polynomial
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial
• Finite-Size Scaling in the Driven Lattice Gas
• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
• Phase transition in the 3-state Potts antiferromagnet on the diced lattice
• A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
• A Neural Networks study of the phase transitions of Potts model
• On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice
• Exact sampling from non-attractive distributions using summary states
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
• The three-state Potts antiferromagnet on plane quadrangulations
• On the generalizability of artificial neural networks in spin models
• Rapid Mixing for Lattice Colorings with Fewer Colors
• Entropy-driven phase transition in low-temperature antiferromagnetic Potts models
• Monte Carlo study of the antiferromagnetic three-state Potts model with staggered polarization field on the square lattice
• Partial order in Potts models on the generalized decorated square lattice
• Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with Staggered Polarization Field
• Sine-Gordon description of the scaling three-state Potts antiferromagnet on the square lattice
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
• Field theory of scaling lattice models. The Potts antiferromagnet
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
• Finite-size investigation of scaling corrections in the square-lattice three-state Potts antiferromagnet square-lattice three-state Potts antiferromagnet