Continuous percolation transition in random cluster growth model

Abstract

A random cluster growth model is developed in terms of two parameters, the initial seed concentration p and the growth probability g of individual clusters. The model is studied on a two dimensional square lattice. For every p value, a critical value of g = gc is determined at which a percolation transition is observed. A scaling theory for this model is developed and numerically verified. The scaling functions are found to scale with p, g as well as the system size L with appropriate critical exponents. The values of the critical exponents are found to belong to the same universality class of percolation. Finally a phase diagram is developed in the p - g parameter space for percolating and non-percolating regions separated by a line of second order phase transition points.