Critical exponents of self-avoiding walks on a family of truncated n-simplex lattices

Abstract

The authors have studied self-avoiding walks (SAWs) on a family of truncated n-simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed. By means of exact renormalisation group transformations, they have calculated the critical exponents nu , alpha and gamma and the connectivity constant mu of the SAWs for n=5 and 6. They propose an approximate theory for calculating the critical exponents of the SAWs on fractals which is expected to be accurate at large values of n. They show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents.