A real space renormalisation group study of the Ising model on self-avoiding walk chains

Abstract

Here the authors apply a small cell, real space renormalisation group technique to study the critical behaviour of the nearest-neighbour interacting Ising model on self-avoiding walk (SAW) chains. In the limit of vanishing interactions between nearest neighbours which are not connected by the walk itself, the treatment reproduces exactly the critical behaviour of the linear chain Ising model. When all the nearest-neighbour interactions are allowed, the treatment gives a vanishing T_c, with the small cells chosen, for the Ising model on SAWS on the square and triangular lattices. The study of the critical behaviour of such models indicates some interesting departures from that of the Ising model on linear chains.