Critical phenomena in disc-percolation model and its application to relativistic heavy ion collisions

TL;DR

This paper introduces a new method to identify critical points in continuum-percolation of discs, which can be applied to determine the deconfinement transition in relativistic heavy ion collisions by analyzing finite-size scaling properties.

Contribution

It proposes using the inflection point of the percolation probability as a novel way to locate critical points and measure critical exponents in heavy ion collision experiments.

Findings

The inflection point of $P_ ext{infty}$ indicates the percolation threshold.

Finite-size scaling of the susceptibility reveals the critical exponent $ u$.

Application to heavy ion collisions allows experimental determination of critical phenomena.

Abstract

Through studying the critical phenomena in continuum-percolation of discs, we find a new approach to locate the critical point, i.e. using the inflection point of $P_\infty$ as an evaluation of the percolation threshold. The susceptibility, defined as the derivative of $P_\infty$, possess finite-size scaling property, where the scaling exponent is the reciprocal of $\nu$ -- the critical exponent of correlation length. The possible application of this approach to the study of the critical phenomena in relativistic heavy ion collisions is discussed. The critical point for deconfinement can be extracted by the inflection point of $P_{\rm QGP}$ -- the probability for the event with QGP formation. The finite-size scaling of its derivative can give the critical exponent $\nu$, which is a rare case that can provide an experimental measure of a critical exponent in heavy ion collisions.