Fluctuation exponents for directed polymers in the intermediate disorder regime

We derive exact fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate scaling regime. This regime corresponds to taking the inverse temperature to zero as the size of the system goes to infinity. The exponents satisfy the KPZ scaling relation and coincide with previous nonrigorous predictions. In the critical case, we recover the fluctuation exponent of the Hopf-Cole solution of the KPZ equation in equilibrium and close to equilibrium.