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

TL;DR

This paper investigates the short-time critical dynamics of percolation observables in the 2D Ising model using Monte Carlo simulations, revealing different behaviors for magnetization and percolation order parameters, with implications for QCD phase transition studies.

Contribution

It provides the first numerical comparison of the dynamic behavior of magnetization and percolation observables in the 2D Ising model during short-time evolution.

Findings

Different dynamic behaviors observed for magnetization and percolation order parameter.

Qualitative differences found between local heat-bath and Swendsen-Wang algorithms.

Results may inform understanding of cluster dynamics in QCD phase transition models.

Abstract

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 Omega, 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.