Dual Monte Carlo and Cluster Algorithms

Abstract

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.

25 pages, 4 figures, to appear in Phys.Rev.E

References in corpus (5)

• Cluster Algorithm for Vertex Models
• Loop algorithms for quantum simulations of fermion models on lattices
• On generalized cluster algorithms for frustrated spin models
• The Loop-Cluster Algorithm for the Case of the 6 Vertex Model
• Virtual Bond Percolation for Ising Cluster Dynamics

Cited by in corpus (24)

• The Loop Algorithm
• Cluster algorithms for general-S quantum spin systems
• Recent Developments of World-Line Monte Carlo Methods
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Invaded cluster algorithm for equilibrium critical points
• Experimental Verification of the Gapless Point in the $S$=1 Antiferromagnetic Bond Alternating Chain
• Magnetization process of the spin-1/2 XXZ models on square and cubic lattices
• Loop updates for quantum Monte Carlo simulations in the canonical ensemble
• Combination of improved multibondic method and the Wang-Landau method
• Can Boltzmann Machines Discover Cluster Updates ?
• Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,
• Low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond-alternation
• Percolation and cluster Monte Carlo dynamics for spin models
• Graphical representations and cluster algorithms for critical points with fields
• Connected component identification and cluster update on GPU
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Broad histogram relation for the bond number and its applications
• Continuous phase transition of a fully frustrated XY model in three dimensions
• Loop Algorithms for Asymmetric Hamiltonians
• Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice
• Percolation and Cluster Formalism in Continuous Spin Systems
• Transition matrix Monte Carlo method for quantum systems
• Reconciling the correlation length for high-spin Heisenberg antiferromagnets
• Novel Monte Carlo algorithms and their applications