In terms of the replica method we consider the low temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows to compute the scaling exponent $\theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $\theta = 1/4$ which is slightly different from the zero-temperature numerical value which is close to $0.241$.
On the scaling properties of (2+1) directed polymers in the high temperature limit
Two-temperature statistics of free energies in (1+1) directed polymers
Free energy fluctuations in Ising spin glasses
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