Directed polymer – directed percolation transition: the strong disorder case
Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Corresponding author: a firstname.lastname@example.org
Revised: 1 October 2004
Published online: 30 March 2005
The transition of physical properties in disordered systems from strong disorder characteristics to weak disorder characteristics is studied for the directed polymer case. It is shown analytically that this transition is governed by the ratio , where ρ is the probability density of the maximal bond of the optimal Min-Max path, pc is the critical probability of directed percolation, and k is the degree of disorder. This analytic result is found to be in agreement with numerical results related to this transition.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005