Real space renormalisation theory of self-avoiding walks on a Manhattan lattice

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Abstract
The real space renormalisation group theory is applied to the self-avoiding walk (SAW) problem on a two-dimensional oriented lattice known as the Manhattan lattice. A finite lattice renormalisation transformation is used to calculate the connectivity constant mu and the size exponent nu . A more general SAW model is defined that contains the oriented and nonoriented lattice problems as special cases. A renormalisation group analysis of this model provides evidence that the SAW on the Manhattan lattice is the same universality class as the ordinary nonoriented SAW problem.