Directed polymers in random media under confining force

Details Directed polymers in random media under confining force Directed polymers in random media under confining force

2005-11-22

arxiv.org/abs/cond-mat/0511564v1

Phys. Rev. E 72, 031803 (2005)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 7 figures

Scientific paper

10.1103/PhysRevE.72.031803

The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by $H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx + \epsilon \Wa^\alpha$, where $\eta(x,y)$ is an uncorrelated random potential and $\Wa$ is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration $R_g(N)$ and the energy fluctuation $\Delta E(N)$ of the polymer of length $N$ in the ground state increase as $R_g(N)\sim N^{\nu}$ and $\Delta E(N)\sim N^\omega$ respectively with $\nu = 1/(1+\alpha)$ and $\omega = (1+2\alpha)/(4+4\alpha)$ for $\alpha\ge 1/2$. A novel algorithm of finding the exact ground state, with the effective time complexity of $\cO(N^3)$, is introduced and used to confirm the conjecture numerically.

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