Critical exponents of self-avoiding walks on fractals with dimension 2-ε
- 1 January 1988
- journal article
- Published by EDP Sciences in Journal de Physique
- Vol. 49 (3) , 397-403
- https://doi.org/10.1051/jphys:01988004903039700
Abstract
We study critical exponents of self-avoiding walks on a family of finitely ramified Sierpinki-type fractals. The members of the family are characterized by an integer b, 2 ≤ b < ∞. For large b, the fractal dimension of the lattice tends to 2 from below. We use scaling theory to determine the critical exponents for large b. We show that as b → ∞ the susceptibility exponent does not tend to its 2-dimensional value, and determine the leading correction to critical exponents for large but finite bKeywords
This publication has 14 references indexed in Scilit:
- Critical exponents for Ising-like systems on Sierpinski carpetsJournal de Physique, 1987
- Large-Scale Properties and Collapse Transition of Branched Polymers: Exact Results on Fractal LatticesPhysical Review Letters, 1986
- Problem of Universality in Phase Transitions on Hierarchical LatticesPhysical Review Letters, 1985
- Simulation of a Critical Ising FractalPhysical Review Letters, 1984
- Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal LatticesPhysical Review Letters, 1983
- Exact Critical Point and Critical Exponents ofModels in Two DimensionsPhysical Review Letters, 1982
- Critical Phenomena on Fractal LatticesPhysical Review Letters, 1980
- Self-avoiding random walks: Some exactly soluble casesJournal of Mathematical Physics, 1978
- Lattices of effectively nonintegral dimensionalityJournal of Mathematical Physics, 1977
- Soluble renormalization groups and scaling fields for low-dimensional Ising systemsAnnals of Physics, 1975