Random potentials for pinning models with Laplacian interactions

TL;DR

This paper studies a polymer model with Laplacian interactions representing stiffness and random potentials modeling media attraction, showing that the critical point gap behavior remains consistent with classical pinning models.

Contribution

It introduces a novel polymer model with Laplacian interactions and analyzes the critical point gap in the presence of randomness, extending pinning model results.

Findings

Critical point gap remains unchanged with randomness.

Laplacian interactions effectively model polymer stiffness.

Results extend classical pinning model theories.

Abstract

We consider a statistical mechanics model for biopolymers. Sophisticated polymer chains, such as DNA, have stiffness when they stretch chains. The Laplacian interaction is used to describe the stiffness. Also, the surface between two media has an attraction force, and the force will pull the chain back to the surface. In this paper, we deal with the random potentials when the monomers interact with the random media. Although these models are different from the pinning models studied before, the result about the gap between the annealed critical point and the quenched critical point stays the same.