New Monte Carlo Algorithms for Classical Spin Systems

We describe a number of recently developed cluster-flipping algorithms for the efficient stimulation of classical spin models near their critical temperature. These include the algorithms of Wolff, Swendsen and Wang, and Niedermeyer, as well as the limited cluster algorithm, the multigrid methods of Kandel and coworkers, and the invaded cluster algorithm. We describe the application of these algorithms to Ising, Potts, and continuous spin models.

• Publication year

  1997

• Venue

  Advances in Chemical Physics

• Publication date

  1997-03-01

• Fields of study

  Physics

• Identifiers
  DOI 10.1002/9780470141649.CH16arXiv cond-mat/9703179
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Dynamic exponent of the two-dimensional Ising model and Monte Carlo computation of the subdominant eigenvalue of the stochastic matrix.

  1996influential reference
• Invaded cluster algorithm for equilibrium critical points.

  1995cited by this paper
• Monte Carlo study of the random-field Ising model.

  1995cited by this paper
• Parallel simulation of the Ising model.

  1994cited by this paper
• The dynamic critical exponent of the three-dimensional Ising model

  1994cited by this paper
• Critical behaviour of the 3D XY-model: a Monte Carlo study

  1993cited by this paper
• Accelerating diffusive nonequilibrium processes in discrete spin systems.

  1993cited by this paper
• Monte Carlo simulations: Hidden errors from "good" random number generators.

  1992cited by this paper
• Empirical relations between static and dynamic exponents for Ising model cluster algorithms.

  1992influential reference
• Cluster Monte Carlo algorithms for random Ising models

  1991cited by this paper
• Comparison of cluster algorithms for two-dimensional Potts models.

  1991influential reference
• Simulations without critical slowing down: Ising and three-state Potts models.

  1989cited by this paper
• Collective Monte Carlo updating for spin systems.

  1989cited by this paper
• General cluster updating method for Monte Carlo simulations.

  1988cited by this paper
• Nonuniversal critical dynamics in Monte Carlo simulations.

  1987cited by this paper
• Monte Carlo study of weighted percolation clusters relevant to the Potts models

  1983cited by this paper
• Critical Dynamics of an Interface in 1+∊ Dimensions

  1981cited by this paper
• On the random-cluster model: I. Introduction and relation to other models

  1972cited by this paper
• Weizmann Institute of Science -- Correspondence, Individual -- letter, 1965-11-07

  1965cited by this paper
• High Temperatures

  1957cited by this paper
• Crystal statistics. I. A two-dimensional model with an order-disorder transition

  1944influential reference

• Simulation of the Three-Component Potts Model on a Hexagonal Lattice by the Monte Carlo Method

  2023cites this paper
• Sampling Algorithms for Discrete Markov Random Fields and Related Graphical Models

  2021cites this paper
• 1D Ising model using the Kronecker sum and Kronecker product

  2020cites this paper
• Theory of Ferroelectric ZrO2 Monolayers on Si

  2019cites this paper
• The hobbyhorse of magnetic systems: the Ising model

  2016cites this paper
• Auxiliary Parameter MCMC for Exponential Random Graph Models

  2016cites this paper
• Cluster and Fast-Update Simulations of Regular and Rewired Lattice Ising Models Using CUDA and Graphical Processing Units

  2010cites this paper
• Structural transitions and dipole moment of water clusters (H2O)(n=4-100).

  2010cites this paper
• Fast and slow dynamics in kinetically constrained models of glasses

  2008cites this paper
• Magnetic behavior of partially filled finite ising surfaces

  2006cites this paper
• Random-Cluster Representation for the Blume–Capel Model

  2000cites this paper
• Epidemics and percolation in small-world networks.

  1999cites this paper
• Scaling and percolation in the small-world network model.

  1999cites this paper