ZERO-TEMPERATURE DIRECTED POLYMERS IN A RANDOM POTENTIAL

Extensive simulations of a model of directed polymers in a random potential are described. The standard deviation DELTA-E(t) of the lowest energy E of walks of t steps varies as t-omega, but there is a large spread in the values quoted in the literature for omega in d = 2 + 1 and 3 + 1. In our model we are able to vary a parameter-the bending energy of the polymer-that affects the apparent value of omega, but, if allowance is made for corrections to scaling, then we find that omega is universal with the value 0.248 +/- 0.004 in d = 2 + 1 and omega = 0.20 +/- 0.01 in d = 3 + 1. The probability distribution P(E,t) is found to scale as t --> infinity, P(E,t)dE --> P(a)da, where a = (E - <E>)/DELTA-E. The scaling function P(a) is investigated and found to be universal, i.e., independent of such details as choice of distribution of the random potential, etc., and in fact identical to within our numerical accuracy to the equivalent distribution of heights in a model of ballistic aggregation.