Critical speeding-up in the local dynamics of the random-cluster model.
We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2, 3 by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S2 exhibits "critical speeding-up": it decorrelates well on time scales much less than one sweep. In some cases the dynamic critical exponent for the integrated autocorrelation time is negative. We also show that the dynamic critical exponent zexp is very close (possibly equal) to the rigorous lower bound alpha/nu and quite possibly smaller than the corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.
Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA.
Youjin
Y
Deng
Timothy M
TM
Garoni
Alan D
AD
Sokal