Scaling Limit of Semiflexible Polymers: A Phase Transition

Abstract

We consider a semiflexible polymer in {{\,\mathrm{{\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.