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Swendsen-Wang simulation of Ising spins and a precise definition of critical clusters

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  • Alexandrowicz, Z.

Abstract

A recent ultrafast simulation of Ising spins (σi = ± 1) utilizes a random + to − flip-over of duly defined decoupled blocks of spins. We show that the random dynamics alone suffices to prove the correspondence of the blocks with “critical clusters” describing thermal (magnetic) fluctuation. (The precise requirement is σiσi = 1, for a pair of spins inside a block, and 〈σiσj〉 = 0, for a σi inside and σj, outside.) The present approach helps to extend the study of critical clusters, and also ultrafast simulation, to the case of nonzero magnetization. Finite critical clusters constitute always a ± symmetric set and are very different (much smaller) than continuous domains of similarly oriented spins.

Suggested Citation

  • Alexandrowicz, Z., 1989. "Swendsen-Wang simulation of Ising spins and a precise definition of critical clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 310-320.
    • Handle: RePEc:eee:phsmap:v:160:y:1989:i:3:p:310-320
    DOI: 10.1016/0378-4371(89)90445-7
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