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

Abstract

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 ≥ 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 → ∞). 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).

Crossover exponent for piecewise directed walk adsorption on Sierpinski fractals

“…At the same time, the lower Bouchaud-Vannimenus boundary φ l (3.24) behaves as 1 − ν for large b, and for all PDW models considered here exponent φ approaches φ l when b → ∞. The same holds for SAW model on n-simplex fractals [29], i.e. φ ≈ φ l when n → ∞, and in the case of simple random walks on d-dimensional Sierpinski gaskets φ is exactly equal to the lower boundary, for any d [30].…”