Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents

TL;DR

This paper investigates the percolation transition in a model of growing clusters on a lattice, identifying a unique universality class through finite size scaling and Monte Carlo simulations.

Contribution

It introduces a detailed analysis of the continuous phase transition in a growing clusters model, revealing a new universality class distinct from standard percolation.

Findings

Determined the percolation threshold for the model.

Measured critical exponents characterizing the transition.

Identified a different universality class from standard percolation.

Abstract

We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration $p$ and a second, non-trivial continuous phase transition for intermediate $p$ values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.