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

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 (Borstnik 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.