Lower-dimensional defect transitions in self-avoiding walks and percolation

The author studies self-avoiding walks and percolation on d-dimensional lattices, focusing on the existence of transitions associated with a defect of dimensionality d* or=2, in contrast to percolation for which they are absent if d*=1. An apparent contradiction with scaling arguments is resolved. A simple renormalisation group approximation yields phase diagrams consistent with these results and provides numerical estimates for crossover exponents and the splitting between 'special' and homogeneous critical points.