Introduction to Cluster Monte Carlo Algorithms

  • E. Luijten
Part of the Lecture Notes in Physics book series (LNP, volume 703)


This chapter provides an introduction to cluster Monte Carlo algorithms for classical statistical-mechanical systems. A brief review of the conventional Metropolis algorithm is given, followed by a detailed discussion of the lattice cluster algorithm developed by Swendsen and Wang and the single-cluster variant introduced by Wolff. For continuum systems, the geometric cluster algorithm of Dress and Krauth is described. It is shown how their geometric approach can be generalized to incorporate particle interactions beyond hardcore repulsions, thus forging a connection between the lattice and continuum approaches. Several illustrative examples are discussed.


Ising Model Detailed Balance Break Bond Pair Energy American Physical Society 
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© Springer 2006

Authors and Affiliations

  • E. Luijten
    • 1
  1. 1.Department of Materials Science and Engineering, Frederick Seitz Materials Research LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.

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