Self-Avoiding Walk on Fractal Complex Networks: Exactly Solvable Cases

Abstract

We study the self-avoiding walk on complex fractal networks called the (u,v)-flower by mapping it to the N-vector model in a generating function formalism. First, we analytically calculate the critical exponent ν and the connective constant by a renormalization-group analysis in arbitrary fractal dimensions. We find that the exponent ν is equal to the displacement exponent, which describes the speed of diffusion in terms of the shortest distance. Second, by obtaining an exact solution for the (u,u)-flower, we provide an example which supports the conjecture that the universality class of the self-avoiding walk on graphs is not determined only by the fractal dimension.

27 pages. arXiv admin note: substantial text overlap with arXiv:1402.0953

References in corpus (4)

• First-passage times in complex scale-invariant media
• Scaling theory of transport in complex networks
• Fractal and Transfractal Recursive Scale-Free Nets
• Probing microscopic origins of confined subdiffusion by first-passage observables

Cited by in corpus (1)

• The Chiral Potts Spin Glass in d=2 and 3 Dimensions