Dynamic Critical Behavior of Percolation Observables in the 2d Ising Model

We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Ω, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables. INTRODUCTION The study of the dynamic critical behavior of simple statistical models might be of relevance for understanding non-equilibrium effects in hot QCD, such as the effects due to heating and cooling of matter produced in heavy-ion collisions. The possible connection [1] between the deconfinement transition in QCD and the percolation phenomenon [2] has received renewed attention recently [3] and the dynamics of cluster observables has been investigated using hysteresis methods [4]. As a preparation for the study of the continuous-spin O(4) model, whose magnetic transition is expected to be in the same universality class of the chiral phase transition in two-flavor QCD, we consider here the short-time dynamics of the 2d Ising model and focus on the dynamic critical behavior of percolation observables. For many physical systems, a suitable definition of cluster provides a mapping of the physical phase transition into the geometric problem of percolation, allowing a better understanding of how the transition is induced in the system. For Ising and O(N) spin models this mapping is well understood [5, 6], whereas in QCD it may be harder to define, even in the pure-gauge case [3]. Given a definition for a cluster on the lattice, the order parameter in percolation theory is the stress of the percolating cluster Ω, defined by