Eur. Phys. J. B 16, 113-117 (2000)
https://doi.org/10.1007/s100510070255

Variation of cluster properties in lattice percolation problem: A prototype of phase transition

National Institute of Chemistry, PO Box 3430, 1001 Ljubljana, Slovenia

Corresponding author: ^a branko@hp10.ki.si

Received: 31 August 1999
Revised: 14 February 2000
Published online: 15 July 2000

Abstract

Properties of clusters appearing in the site percolation problem on square and cubic lattices are expressed in a way that emphasizes the thermodynamic analogy. It is shown that the analog of the specific heat exhibits expected critical behaviour as a function of the analog of the temperature. The results support the notion that the partition of the specific heat of Ising systems (Borštnik and Lukman, Phys. Rev. E 60, 2595 (1999)) into the structural and populational component is a meaningful one. Another cluster property which is taken under the scrutiny is the fractal dimensionality of clusters which also indicates the presence of phase transition.