Critical exponent for the loop erased self-avoiding walk by Monte Carlo methods

Abstract

A Monte Carlo simulation was performed for loop-erased self-avoiding walks (LESAW) to ascertain the exponent v for the Z2 and Z3 lattices. The estimated values were 2 v=1.600±0.006 in two dimensions and 2 v=1.232±0.008 in three dimensions, leading to the conjecture v=4/5 for the two-dimensional LESAW. These results add to existing evidence that the loop-erased self-avoiding walks are not in the same universality class as self-avoiding walks. © 1990 Plenum Publishing Corporation.