CRITICALITY OF SELF-AVOIDING WALKS WITH AN EXCLUDED INFINITE NEEDLE

We study the effect of repulsion for self-avoiding walks and random walks from excluded sets. We show, in particular, that the mean displacement away from an excluded infinite needle of self-avoiding random walks in three dimensions has to diverge along the privileged axis as N-sigma, where N is the number of steps and sigma is a sub-leading critical exponent for the two-point function. This exponent has been determined by using a high-precision Monte Carlo simulation (sigma = 0.370 +/- 0.011). Its knowledge is used to improve the measure of universal quantities, like the exponent nu (nu = 0.5867 +/- 0.0025, in agreement with the epsilon-expansion estimate and with experimental data) and amplitude ratios. We verify also that for simple random walks the excluded needle introduces instead logarithmic violations to scaling.