Dual Geometric Worm Algorithm for Two-Dimensional Discrete Classical Lattice Models

Abstract

We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof'ev and Svistunov \cite{ProkofevClassical}. The algorithm is defined on the dual lattice and is formulated in terms of bond-variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond-variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be "directed" by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.

12 pages, 6 figures, Revtex 4

References in corpus (9)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Quantum Monte Carlo with Directed Loops
• Worm algorithms for classical statistical models
• Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• Monte Carlo study of the random-field Ising model
• Invaded cluster algorithm for equilibrium critical points
• Directed geometrical worm algorithm applied to the quantum rotor model
• Direct Monte Carlo Measurement of the Surface Tension in Ising Models

Cited by in corpus (10)

• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions
• A Worm Algorithm for Two-Dimensional Spin Glasses
• The worm process for the Ising model is rapidly mixing
• Geometric allocation approach to accelerating directed worm algorithm
• Statistical properties of worm algorithms for two dimensional frustrated Ising models
• Flux roughening in spin ice with mixed $\pm J$ interactions
• Avoiding critical slowdown in models with SALR interactions
• Exploring the worldline formulation of the Potts model
• Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees