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

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∞ as an evaluation of the percolation threshold. The susceptibility, defined as the derivative of P∞, possess finite-size scaling property, where the scaling exponent is the reciprocal of ν -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 PQGP -the probability for the event with QGP formation. The finite-size scaling of its derivative can give the critical exponent ν, which is a rare case that can provide an experimental measure of a critical exponent in heavy ion collisions.

The universality class of random searches in critically scarce environments

“…Usually, for finite size systems λ inf and λc are correlated and close to each other [28], with λ inf → λc at the thermodynamic limit. Also, in the finite size case the fluctuations are higher just at λ inf [29]. (λ c , β/ν // ) when λ → λ c .…”