Directed polymers with random interaction: marginal relevance and novel criticality

Abstract

We show by an exact renormalization-group approach that a random two-chain interaction for (d+1)-dimensional directed polymers is marginally relevant at d=1. There is a critical point for d>1 separating the weak and strong disorder phases, and the length scale exponent is v=[2(d-1)]^-1 for d>1. For the mth-order multicritical case involving random m-chain interactions, the disorder is marginally relevant at d_m=1/(m-1). Here also the disorder induces a critical point for d>d_m, with an exponent v_m=[2d(m-1)-2]^-1. An essential singularity occurs for the length scale right at d=d_m.