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

By 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 ∞, possesses a finite-size scaling property, where the scaling exponent is the reciprocal of v , the critical exponent of the correlation length. A 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 QGP — the probability for the event with QGP formation. The finite-size scaling of its derivative can give the critical exponent v , which is a rare case that can provide an experimental measure of a critical exponent in heavy ion collisions.