A polymer in a multi-interface medium

TL;DR

This paper analyzes a polymer model interacting with multiple interfaces, revealing a phase transition at interface spacing proportional to logarithm of polymer length, using renewal theory for explicit scaling behavior.

Contribution

It provides the first explicit characterization of the scaling limits and phase transition in a polymer-interface interaction model with variable interface spacing.

Findings

Transition at interface spacing T_N=O(log N)

Explicit scaling behavior determined

Renewal theory applied successfully

Abstract

We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity $\delta \in \mathbb {R}$ of the pinning interaction is constant, while the interface spacing $T=T_N$ is allowed to vary with the size $N$ of the polymer. Our main result is the explicit determination of the scaling behavior of the model in the large $N$ limit, as a function of $(T_N)_N$ and for fixed $\delta >0$. In particular, we show that a transition occurs at $T_N=O(\log N)$. Our approach is based on renewal theory.