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.

arXiv comment7 pages

References in corpus (23)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Free-energy distribution of the directed polymer at high temperature
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• The crossover regime for the weakly asymmetric simple exclusion process
• Probability distribution of the free energy of a directed polymer in a random medium
• Directed polymer near a hard wall and KPZ equation in the half-space
• Chaos in temperature in the Sherrington-Kirkpatrick model
• Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments
• Two-point free energy distribution function in (1+1) directed polymers
• Temperature and Disorder Chaos in Low Dimensional Directed Paths
• Two-time free energy distribution function in (1+1) directed polymers
• On the equal time two-point distribution of the one-dimensional KPZ equation by replica
• On two-time distribution functions in (1+1) random directed polymers
• $N$-point free energy distribution function in one dimensional random directed polymers
• Ultrametricity Between States at Different Temperatures in Spin-Glasses
• Temperature chaos and quenched heterogeneities