Two-temperature statistics of free energies in (1+1) directed polymers

The joint statistical properties of two free energies computed at two different temperatures in the same sample of (1 + 1) directed polymers is studied in terms of the replica technique. The scaling dependence of the reduced free-energies difference F = F(T-1)/T-1 - F(T-2)/T-2 on the two temperatures T1 and T2 is derived. In particular, it is shown that if the two temperatures T-1 < T-2 are close to each other, the typical value of the fluctuating part of the reduced free-energies difference F is proportional to (1 - T-1/T-2)(1/3). It is also shown that the left-tail asymptotics of this free-energy difference probability distribution function coincides with the corresponding tail of the TW distribution. Copyright (C) EPLA, 2016