Depinning of a polymer in a multi-interface medium

TL;DR

This paper analyzes the depinning transition of a polymer interacting with multiple equi-spaced interfaces, revealing two critical scaling regimes as the interface spacing grows with the polymer size.

Contribution

It introduces a model for a polymer repelled by multiple interfaces and identifies two new scaling transition points based on the interface spacing growth.

Findings

Two transition points at T_N ≈ N^{1/3} and T_N ≈ N^{1/2}

Scaling behavior depends on the growth rate of interface spacing

Uses renewal theory techniques for analysis

Abstract

In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of the polymer. When the polymer receives a positive reward for touching the interfaces, its asymptotic behavior has been derived in a previous paper, showing that a transition occurs when T_N \approx log(N). In the present paper, we deal with the so-called depinning case, i.e., the polymer is repelled rather than attracted by the interfaces. Using techniques from renewal theory, we determine the scaling behavior of the model for large N as a function of T_N, showing that two transitions occur, when T_N \approx N^{1/3} and when T_N \approx N^{1/2} respectively.