LOW-TEMPERATURE PROPERTIES OF DIRECTED WALKS WITH RANDOM SELF-INTERACTIONS

We consider a simple model for a chain with random self-interactions. Each monomer on the chain carries a charge, which is a random variable, and the configurations of the chain are directed walks. We show that at zero temperature the end-to-end distance R and the energy E of chains with total charge Q is similar to N(x) scale as R is similar to N(nu(x)) and E is similar to N(theta(x)). The exponents thus depend on the total charge through the parameter x. These exponents are measured numerically and compared to the predictions of some simple arguments. At a finite temperature, R is extensive and appears to be independent of x.