Directed polymers in a random environment with a defect line

Abstract

We study the depinning transition of the $1+1$ dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site of ${\mathbb{Z}}^2$; sites on the positive axis have the potential enhanced by a deterministic value $u$. We show that for small inverse temperature $\beta$ the quenched and annealed free energies differ significantly at most in a small neighborhood (of size of order $\beta$) of the annealed critical point $u_c^a=0$. For the case $u=0$, we show that the difference between quenched and annealed free energies is of order ${\beta }^4$ as $\beta \to 0$, assuming only finiteness of exponential moments of the potential values, improving existing results which required stronger assumptions.

22 pages. Changes to Proposition 3.8 make Proposition 4.1 unnecessary; minor corrections made

References in corpus (3)

• Last Passage Percolation with a Defect Line and the Solution of the Slow Bond Problem
• Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment
• Polymer pinning in a random medium as influence percolation

Cited by in corpus (7)

• Last Passage Percolation with a Defect Line and the Solution of the Slow Bond Problem
• Localization of directed polymers with general reference walk
• The scaling limit of the directed polymer with power-law tail disorder
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
• Directed polymers on a disordered tree with a defect subtree
• Free energy of directed polymers in random environment in $1+1$-dimension at high temperature
• Two-sided bounds on free energy of directed polymers on strongly recurrent graphs