Croatica Chemica Acta, Vol. 86 No. 4, 2013.
Izvorni znanstveni članak
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
Sažetak
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)
Ključne riječi
percolation; random cluster growth; variable initial conditions; continuous transitions; universality class
Hrčak ID:
112788
URI
Datum izdavanja:
16.12.2013.
Posjeta: 1.493 *