Directed polymers with random interaction: Marginal relevance and novel criticality

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 {ν}=[2(d-1)]^-1 for d>1. For the mth-order multicritical case involving random m-chain interactions, the disorder is marginally relevant at dₘ=1/(m-1). Here also the disorder induces a critical point for d>dₘ, with an exponent νₘ=[2d(m-1)-2]^-1. An essential singularity occurs for the length scale right at d=dₘ.