Critical properties of various sizes of cluster in the Ising percolation transition

TL;DR

This paper investigates the critical properties of clusters in the Ising model to identify phase transition points, using finite size scaling and statistical measures, with potential applications to QCD and heavy-ion collisions.

Contribution

It systematically studies cluster correlations and fluctuations in the Ising model to develop methods for locating critical points applicable to QCD phase transitions.

Findings

Skewness and kurtosis of cluster sizes are size-independent at criticality.

Finite size scaling and fixed point analysis effectively identify the critical point.

Universal behavior of order parameter fluctuations is observed.

Abstract

It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed.