Single-cluster dynamics for the random-cluster model

Single-cluster dynamics for the random-cluster model

Deng, Y.
Qian, X.
Blöte, H.W.J.

Applied Sciences

2009-09-30

We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full-cluster decomposition of random-cluster configurations. We explore the critical dynamics of this algorithm for several two-dimensional Potts and random-cluster models. For integer q, the single-cluster algorithm can be reduced to the Wolff algorithm, for which case we find that the autocorrelation functions decay almost purely exponentially, with dynamic exponents zexp=0.07 (1), 0.521 (7), and 1.007 (9) for q=2, 3, and 4, respectively. For noninteger q, the dynamical behavior of the single-cluster algorithm appears to be very dissimilar to that of the SWCM algorithm. For large critical systems, the autocorrelation function displays a range of power-law behavior as a function of time. The dynamic exponents are relatively large. We provide an explanation for this peculiar dynamic behavior.

http://resolver.tudelft.nl/uuid:48e63a2f-fc8a-44f5-8aa4-303a141db4b0

https://doi.org/10.1103/PhysRevE.80.036707

American Physical Society

1539-3755

Physical Review E, 80 (3), 2009

Institutional Repository

journal article

(c) 2009 The Authors ; American Physical Society