Self-avoiding walk connectivity constant and theta point on percolating lattices

Abstract

The average connectivity constant mu of self-avoiding walks (SAWs) is obtained from exact enumeration of SAWs on Monte Carlo generated percolating clusters in a randomly diluted square lattice. For averages over the (infinite) percolating cluster, mu decreases almost linearly with bond dilution (1-p), where p is the bond occupation concentration. The authors find mu (p_c)=1.31+or−0.03 at the percolation threshold p_c and could not detect any significant difference between mu (p_c) and p_c mu (1). The variation of theta-point for SAWs on the same lattice with dilution is also estimated, analysing the partition function zeros. Within the limited accuracy of their analysis, its variation with dilution is observed as being quite weak and the theta-point increases somewhat (compared to pure lattice value) near p_c; they find a non-vanishing theta point (K_theta (p_c) equivalent to 0.59, where K₀=J/k theta ) on the square lattice percolation cluster at p_c.