04-02E

# 04-02E

By - Posted on 08 February 2012

UDC:
530.145
PACS:
64.60.Ak, 64.60.Fr, 05.50.+q

Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

C. von Ferber
V. Blavats'ka
R. Folk
Yu. Holovatch

The scaling properties of self-avoiding walks on a $d$- dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B. Harris (Phys. Rev. Lett., {\bf 63}, 2819 (1989)). While the former first order perturbation did not agree with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent $\nu _{\rm p}={1}/{2}+{\varepsilon }/{42}+ {110}\varepsilon ^2/{21^3}$, $\varepsilon =6-d$. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions $2\leq d \leq 6$.

Year:
2004
Pages:
9