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

Victor Dotsenko

Published 2016-11-21Version 1

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 free energy difference on the two temperatures 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 free energy difference is proportional to $(1 - T_{1}/T_{2})^{1/3}$. It is also shown that the left tail asymptotics of the free energy difference probability distribution function coincides with corresponding tail of the TW distribution.