Scale-free network hidden in a collapsing polymer

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 cutoff degree dc proportional to L(2-c), where is the loop exponent for dense polymers (c=11/8 in two dimensions) and is the length of the polymer. Our results exemplify how a scale-free network can emerge from standard criticality.