Critical exponents of the self-avoiding walks on a family of finitely ramified fractals

Abstract

The authors have studied the self-avoiding walks (SAW) on a family of finitely ramified fractals. The first member (b=2) of the family is the two-dimensional Sierpinski gasket, while the last member (b= infinity ) appears to be a wedge of the homogeneous triangular lattice. By means of the exact renormalisation group transformations they have calculated the critical exponents alpha , nu and gamma , and the connectivity constant mu , of SAW on each member of a sequence (2<or=b<or=8) of the studied fractal family. The obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two-dimensional lattice.