A direct renormalization group approach for the excluded volume problem

We propose a position-space renormalization group approach for the excluded volume problem in a square lattice by considering “percolating” self-avoiding paths in ab×b cell, whereb=2,3,4: Two ways of counting the paths are presented. The values obtained for the exponentv converge respectively to 0.731 and 0.720, close to the usually accepted valuev=0.75. Comments on the relation between percolation and self-avoiding walks are made.