Self-avoiding walks on diluted networks

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Abstract
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.

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