Finite size scaling study of a two parameter percolation model

TL;DR

This paper introduces a two-parameter percolation model with nucleation and growth, develops a finite size scaling theory, and finds that it shares the same universality class as traditional percolation.

Contribution

It develops and verifies a finite size scaling theory for a novel two-parameter percolation model with nucleation and growth.

Findings

Scaling functions depend on both parameters g and ρ

Critical exponents match those of original percolation

Model belongs to the same universality class as standard percolation

Abstract

A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final static configuration of spanning clusters. A finite size scaling theory for such transition is developed and numerically verified. The scaling functions are found to depend on both g and \rho. The singularities at the critical growth probability gc of a given \rho are described by appropriate critical exponents. The values of the critical exponents are found to be same as that of the original percolation at all values of \rho at the respective gc . The model then belongs to the same universality class of percolation for the whole range of \rho.