Original scientific paper

https://doi.org/10.5562/cca2313

Continuous Percolation Transition in Random Cluster Growth Model

Bappaditya Roy ; Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India
Sitangshu Bikas Santra ; Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India

Abstract

A random cluster growth model is developed in terms of two parameters, the initial seed concentration
ρ and the growth probability g of individual clusters. The model is studied on a two dimensional
square lattice. For every ρ 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 ρ, 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 ρ − g parameter space for percolating and non-percolating regions separated by a
line of second order phase transition points. (doi: 10.5562/cca2313)

Keywords

percolation; random cluster growth; variable initial conditions; continuous transitions; universality class

Hrčak ID:

112788

URI

https://hrcak.srce.hr/112788

Publication date:

16.12.2013.

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