Using the Monte Carlo simulation method, we calculate the particle density $\rho$, the density fluctuation $F$, the percolation ratio $P$, and the mean cluster size $S$ as a function of $p$, where $p=\frac{e^{\Delta }}{(e^{\Delta }+1)}$, with $\Delta$ being the chemical potential, for hard-core particles on the plane triangular and the square lattices with pure excluded-volume interactions. In each studied case the singular point is consistent with the percolation transition point within numerical errors. Our results indicate that the phase transitions of the studied systems are percolation transitions.

• Received 17 August 1988

DOI:https://doi.org/10.1103/PhysRevB.39.2948