Scaling of fluctuation for Directed polymers with random interaction

Using a finite size scaling form for reunion probability, we show numerically the existence of a binding-unbinding transition for Directed polymers with random interaction. The cases studied are (A1) two chains in 1+1 dimensions, (A2) two chains in 2+1 dimensions and (B) three chains in 1+1 dimensions. A similar finite size scaling form for fluctuation establishes a disorder induced transition with identical exponents for cases A2 and B. The length scale exponents in all the three cases are in agreement with previous exact renormalization group results.