Series studies of self-avoiding walks near the theta -point on 2D critical percolation clusters

The thermally weighted average end-to-end distance (R_N) of interacting self-avoiding walks (SAWs) are obtained enumerating all the (finite) N-stepped SAW configurations on the infinite percolation cluster of bond diluted square lattice at the percolation threshold. Averaging over 250 percolation clusters and enumerating all the possible SAWs on them for N up to 31, (R_N) is fitted to a scaling form (R²_N) approximately N^{2 nu theta} f(N^phi tau )=(T-^theta )/^theta is the temperature interval away from the ^theta -point, phi is the crossover exponent and nu theta is the tricritical size exponent. The best fit is obtained for ^theta approximately=0.71 (compared to ^theta ₀ approximately=1.54 on a pure square lattice), nu approximately=0.74 (compared to nu ^theta _phi =4 mod 7 approximately=0.57 in two dimensions) and phi approximately=0.20. They also obtain an estimate for of SAW size exponent nu ^C for collapsed phase on the percolation cluster.