On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice

Abstract

We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at zero temperature. We prove that this algorithm is not ergodic for symmetric subsets of the kagome lattice with fully periodic boundary conditions: given an initial configuration, not all configurations are accessible via Monte Carlo steps. The same conclusion holds for single-site dynamics.

arXiv commentLatex2e. 22 pages. Contains 11 figures using pstricks package. Uses iopart.sty. Final version accepted in journal

References in corpus (7)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study
• A constrained Potts antiferromagnet model with an interface representation
• Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach
• A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
• Comment on ``Antiferromagnetic Potts Models''

Cited by in corpus (12)

• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Resonating color state and emergent chromodynamics in the kagome antiferromagnet
• Heterogeneous freezing in a geometrically frustrated spin model without disorder: spontaneous generation of two time-scales
• Worm Monte Carlo study of the honeycomb-lattice loop model
• Monopole holes in a partially ordered spin liquid
• Colorings of odd or even chirality on hexagonal lattices
• Q-colourings of the triangular lattice: Exact exponents and conformal field theory
• The three-state Potts antiferromagnet on plane quadrangulations
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
• Hamiltonian cycles and 1-factors in 5-regular graphs
• Invariants of winding-numbers and steric obstruction in dynamics of flux lines