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

Abstract

The joint statistical properties of two free energies computed at two different temperatures in {\it 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 $\mathcal{F}=F(T_1)/T_1-F(T_2)/T_2$ on the two temperatures $T_1$ and $T_2$ 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 $\mathcal{F}$ 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.

7 pages

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• An exact solution for the KPZ equation with flat initial conditions
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• $N$-point free energy distribution function in one dimensional random directed polymers