Critical exponents of surface-interacting self-avoiding walks on a family of truncated n-simplex lattices

Details Critical exponents of surface-interacting self-avoiding walks on a family of truncated n-simplex lattices Critical exponents of surface-interacting self-avoiding walks on a family of truncated n-simplex lattices

1996-12-27

arxiv.org/abs/cond-mat/9612233v1

Physica A 227 (1996) 213-233

Physics

Condensed Matter

Statistical Mechanics

25 pages, Tex, 8 figures (eps)

Scientific paper

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer $n\ge 3$. Using the exact renormalization group method we have been able to obtain the exact values of various critical exponents for all values of n up to n=6. We also derived simple formulas which describe the asymptotic behavior of these exponents in the limit of large n ($n\to\infty$). In spite of the fact that the coordination number of the lattice tends to infinity in this limit, we found that the most of the studied critical exponents approach certain finite values, which differ from corresponding values for simple random walks (without self-avoiding walk constraint).

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