  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 $\ge 2$.
