Abstract
Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimension Dsaw is affected by disorder is introduced. Using this method, it is found that for some lattices, Dsaw is unaffected by weak disorder; while for others Dsaw changes even for infinitestimal disorder. A weak disorder exponent λ is defined and calculated analytically [λ measures the dependence of the variance in the partition function (or in the effective fugacity per step)v∼Lλ on the end-to-end distance of the SAW, L]. For lattices which are stable against weak disorder (λ<0) a phase transition exists at a critical value v=v* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of λ are discussed.
Original language | English |
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Pages (from-to) | 147-167 |
Number of pages | 21 |
Journal | Journal of Statistical Physics |
Volume | 80 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Jul 1995 |
Externally published | Yes |
Keywords
- Self-avoiding walks
- disordered environment
- fractals
- hierarchical lattices
- renormalization
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics