Spiral site percolation on the square and triangular lattices

Abstract

Percolation under rotational constraint is studied on the square and triangular lattices by three different methods: finite-size scaling study, Monte Carlo simulation and series expansion. The critical percolation probability p_c and some critical exponents are determined. Evidence is obtained for a scaling form of the cluster distribution function. For the square lattice, the average cluster size exponent gamma is found to be equal to that of directed percolation.