Spectral dimension and the shortest path of SAW s with multi-neighbour interactions

Abstract

The spectral dimension and the shortest path of self-avoiding walks (SAWs) with bridge length (interaction range) b=1, 2, 3, 2 are studied numerically. The spectral dimension is calculated by performing exact multi-neighbour random walks on the Monte Carlo generated SAW configurations. It is found that the spectral dimension is not affected by the finite range of interactions (finite bridge length), and approach to d_s=1 both in dimensions d=2 and 3. The shortest path length S_N of the N-step SAW with local bridges is also investigated. It is shown that S_N/N=A+N^{- Delta} (B+C/N). The authors' numerical simulation results indicate that the exponent Delta is independent of the dimensionality, and is about 3/16 in dimensions d=2-5.