Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5):051123. doi: 10.1103/PhysRevE.74.051123. Epub 2006 Nov 28.

Short-time dynamics of percolation observables.

Physical review. E, Statistical, nonlinear, and soft matter physics

Wanderson G Wanzeller, Tereza Mendes, Gastão Krein

PMID: 17279893 DOI: 10.1103/PhysRevE.74.051123

Abstract

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Publication Types

• Journal Article