Collapse of percolation clusters — A transfer matrix study

Abstract

Exact calculations using transfer matrices on finite strips are performed to study the two-dimensional problem of site percolation clusters with an attractive nearest neighbor interaction. Thermodynamic quantities such as free energy per site and specific heat are calculated. Finite-size scaling with two strips of different widths yields very accurate approximations of the critical line and the correlation length exponent. The result shows clearly a site percolation fixed point at very high temperatures, a random animal fixed point at intermediate temperatures, aΘ point for the collapse of lattice animals at lower temperatures, and a compact-cluster fixed point at the lowest temperatures.