Finite-size correction in a disordered system: a new divergence

Abstract

We show that the amplitude of the finite-size correction term for the nth moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as (n_c-n)^-r, as a critical moment n_c is approached. The exponent r is independent of temperature but does depend on the effective dimensionality. There is no such divergence on the low temperature side (n>n_c).