Scaling limit of semiflexible polymers: a phase transition

TL;DR

This paper investigates how the scaling limit of a semiflexible polymer in a lattice changes with parameters, revealing a phase transition between Gaussian free field, mixed distribution, and membrane model regimes.

Contribution

It establishes a phase transition in the scaling limit of semiflexible polymers based on the interplay of gradient and Laplacian interactions.

Findings

Scaling limit is Gaussian free field in one regime.

Scaling limit becomes a mixed distribution in another regime.

Continuum membrane model appears as the limit in a different regime.

Abstract

We consider a semiflexible polymer in $\mathbb Z^d$ which is a random interface model with a mixed gradient and Laplacian interaction. The strength of the two operators is governed by two parameters called lateral tension and bending rigidity, which might depend on the size of the graph. In this article we show a phase transition in the scaling limit according to the strength of these parameters: we prove that the scaling limit is, respectively, the Gaussian free field, a "mixed" random distribution and the continuum membrane model in three different regimes.