Transition to Localization of Biased Walkers in a Randomly Absorbing Enviroment

Details Transition to Localization of Biased Walkers in a Randomly Absorbing Enviroment Transition to Localization of Biased Walkers in a Randomly Absorbing Enviroment

2001-07-25

arxiv.org/abs/cond-mat/0107525v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 13 figures; 1 reference added

Scientific paper

10.1016/S0167-2789(02)00513-4

We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic drift velocity of survivors which is zero below a critical bias. This transition is second-order in one dimension but of first order in higher dimensions. The model can be mapped to a stretched polymer with attractive interaction between monomers, and this phase transition would then describe sudden unfolding of the polymer when the stretching force exceeds a critical value. We also present precise simulations of the zero bias case where we show unambiguously that the transition between the Rosenstock and Donsker-Varadhan regimes is first order in dimension $\ge 2$.

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