Self-avoiding walks on diluted networks

It is shown that, contrary to recent suggestions, the exponent {ν}, characterizing self-avoiding walks in a diluted lattice at the percolation threshold, is determined by a fixed point, different from the pure latttice one. The full phase diagram of this system is obtained by a real-space renormalization group and five nontrivial fixed points are identified. A field-theoretical treatment yields {ν}=(1/2+{ε}/42, with {ε}=6-d. All these results are supported by exact enumeration analysis.