Spanning trees for the geometry and dynamics of compact polymers

TL;DR

This paper models compact polymers using spanning trees on the Manhattan lattice, calculating their average bends, energy, and dynamics, revealing universal relaxation mechanisms and aging phenomena.

Contribution

It introduces a novel mapping of compact polymers to spanning trees, enabling exact calculations and analysis of their relaxation and aging behaviors.

Findings

Exact average number of bends at infinite temperature

Energy as a function of bending rigidity and elasticity

Observation of aging and domain coarsening after temperature quenches

Abstract

Using a mapping of compact polymers on the Manhattan lattice to spanning trees, we calculate exactly the average number of bends at infinite temperature. We then find, in a high temperature approximation, the energy of the system as a function of bending rigidity and polymer elasticity. We identify the universal mechanism for the relaxation of compact polymers and then endow the model with physically motivated dynamics in the convenient framework of the trees. We find aging and domain coarsening after quenches in temperature. We explain the slow dynamics in terms of the geometrical interconnections between the energy and the dynamics.