High-density site percolation on real lattices

In high-density site percolation, attention is centred only on those clusters consisting of occupied sites with a given minimum number m of occupied neighbours. The authors study this problem on square, triangular and cubic lattices using Monte Carlo computer simulations and generate several new results. High-density site percolation thresholds are given to moderate accuracy for all relevant values of m on the three lattices considered. They also find their results consistent with universality as the integer m is varied. Specifically, the critical exponents beta and gamma are shown to be determined mainly by the dimensionality d of the lattice in question and insensitive to variations in the value of the parameter m.

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