caa a22 4500 467892903 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061001xx s 000 0 eng 10.1007/s10955-006-9098-7 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9098-7 Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals [Elektronische Daten] [Sumedha,, Deepak Dhar] We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W n (S), and rooted self-avoiding polygons P n (S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P n (S), and W n(S) for an arbitrary point S on the lattice. These are used to compute the averages $$\langle P_{n}(S) \rangle$$ , $$\langle W_{n}(S) \rangle$$ , $$\langle \log P_{n}(S) \rangle$$ and $$\langle \log W_{n}(S) \rangle$$ over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent $$\nu$$ are the same for the annealed and quenched averages. However, $$\langle \log P_{n}(S) \rangle \simeq n \log \mu + (\alpha_q - 2)\log n$$ , and $$\langle \log W_{n}(S) \rangle \simeq n \log \mu + (\gamma_q-1) log{n}$$ , where the exponents $$\alpha_q$$ and $$\gamma_q$$ , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives $$\alpha_q \simeq 0.72837 \pm 0.00001;$$ and $$\gamma_q \simeq 1.37501 \pm 0.00003$$ , to be compared with the known annealed values $$\alpha_a = 0.73421$$ and $$\gamma_q = 1.37522$$ . Springer Science+Business Media, Inc., 2006 self-avoiding walks nationallicence random media nationallicence fractals nationallicence Sumedha, Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, 400005, Mumbai, India aut Dhar Deepak Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, 400005, Mumbai, India aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/1(2006-10-01), 55-76 0022-4715 125:1<55 2006 125 10955 https://doi.org/10.1007/s10955-006-9098-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9098-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sumedha Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, 400005, Mumbai, India aut NATIONALLICENCE 700 1- Dhar Deepak Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, 400005, Mumbai, India aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/1(2006-10-01), 55-76 0022-4715 125:1<55 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer