Polymer in a multi-interface medium with weak repulsion

TL;DR

This paper extends the study of long polymers in multi-interface environments by analyzing the effects of increasing temperature and interface distance, revealing new behaviors and providing a comprehensive phase diagram.

Contribution

It introduces a novel extension of the polymer model with variable temperature and interface spacing, and establishes a full phase diagram with new behavioral insights.

Findings

New phase behavior emerges at high temperature and large interface distance.

Sharp results on simple random walk between interfaces are developed.

A complete phase diagram for the extended model is provided.

Abstract

Long linear polymers in a depinned interfaces environment have been studied for a long time, for instance in \cite{Caravenna2009depinning} when the temperature is constant. In this paper, we study an extension of this model by making the temperature and the distance between interfaces goes to infinity. We give a full phase diagram for this model, and show that a new behaviour appears in this extension. Our key tool include new sharp results on the simple random walk evolving between interfaces.