A scale-free network hidden in the collapsing polymer

TL;DR

This paper reveals that the contact network within a collapsed polymer forms a scale-free network characterized by a specific degree distribution, illustrating how critical phenomena can give rise to complex network structures.

Contribution

It demonstrates the emergence of a scale-free incompatibility graph in the collapsed phase of polymers, linking polymer criticality to network theory.

Findings

Degree distribution follows a power-law decay with exponent γ = 1/(2-c)

Cut-off degree scales as L^{2-c} with polymer length L

Scale-free network emerges from standard polymer criticality

Abstract

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $\gamma = 1/(2-c)$ up to a cut-off degree $d_c \propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.