Directed polymer - Directed percolation transition: The strong disorder case

The transition of physical properties in disordered systems from strong disorder characteristics to weak disorder characteristics is studied for the directed polymer case. It is shown analytically that this transition is governed by the ratio ρ(pc)/k, where ρ is the probability density of the maximal bond of the optimal Min-Max path, pc is the critical probability of directed percolation, and k is the degree of disorder. This analytic result is found to be in agreement with numerical results related to this transition.