Directed Random Walk on the Lattices of Genus Two

Abstract

The object of the present investigation is an ensemble of self-avoiding and directed graphs belonging to eight-branching Cayley tree (Bethe lattice) generated by the Fucsian group of a Riemann surface of genus two and embedded in the Pincaré unit disk. We consider two-parametric lattices and calculate the multifractal scaling exponents for the moments of the graph lengths distribution as functions of these parameters. We show the results of numerical and statistical computations, where the latter are based on a random walk model.

17 pages, 8 figures

References in corpus (1)

• Multifractality of self-avoiding walks on percolation clusters

Cited by in corpus (3)

• Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
• Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two
• Structures associated with the Borromean rings complement in the Poincaré ball