Overlaps of successive configurations or clusters in Wolff and Swendsen-Wang Monte Carlo algorithms act as order parameters that reflect the critical thermodynamics of Ising and Potts models, unlike local Metropolis flips.
Wolff, Collective Monte Carlo Updating for Spin Sys- tems, Physical Review Letters62, 361 (1989)
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Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena
Overlaps of successive configurations or clusters in Wolff and Swendsen-Wang Monte Carlo algorithms act as order parameters that reflect the critical thermodynamics of Ising and Potts models, unlike local Metropolis flips.