Publication record · 18.cifr/1987.swendsen.sw-cluster-mc

Nonuniversal critical dynamics in Monte Carlo simulations

v1.0.0

Robert H. Swendsen (Carnegie Mellon University), Jian-Sheng Wang (Carnegie Mellon University)

RAI18.cifr/1987.swendsen.sw-cluster-mc

Physical Review Letters· 1987· doi:10.1103/PhysRevLett.58.86

A new approach to Monte Carlo simulations is presented which eliminates critical slowing down for a class of models. The method uses a nonlocal updating scheme based on the Fortuin-Kasteleyn representation of the Potts model. By flipping clusters of spins simultaneously the dynamic critical exponent z is reduced from approximately 2 to approximately 0, demonstrating nonuniversal critical dynamics.

Monte Carlocritical slowing downcluster algorithmPotts modelFortuin-Kasteleyn

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Conventional single-spin-flip Monte Carlo suffers critical slowing down near second-order transitions (tau ~ L^z, z~2), making large systems intractable. The SW algorithm operates on mesoscopic clusters, reducing autocorrelation times by orders of magnitude at the critical temperature.

Novelty

Swendsen and Wang introduced a cluster-flip Monte Carlo algorithm that groups spins into clusters via FK bond percolation and flips entire clusters simultaneously. This eliminates critical slowing down near phase transitions (z~0 vs conventional z~2). The method is exact and satisfies detailed balance.

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