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 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).