Polymer Collapse on Fluctuating Random Surfaces

TL;DR

This paper models the behavior of polymers on fluctuating random surfaces using a two-matrix approach, revealing a third-order collapse transition at a specific interaction strength with universal scaling laws.

Contribution

It provides an exact partition function for self-avoiding chains on dynamical surfaces, identifying the collapse transition and universal scaling laws.

Findings

Polymer undergoes a third-order collapse transition at c=√2 - 1.

Derived exact partition function for polymers on random surfaces.

Identified universal scaling laws for the transition.

Abstract

The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact interactions of relative strength $1/c$, $0<c<1$, is found as a function of chain length $L$ and $c$. The number of configurations $L^a {\rm e}^{bL}$ as $L\to \infty$ is determined, showing that a chain undergoes a third-order collapse transition at $c=\sqrt{2} -1$; the universal scaling laws are found.