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 $d_c\propto L^{2-c}$, 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 can emerge from standard criticality.

• Received 22 September 2004

DOI:https://doi.org/10.1103/PhysRevE.72.055102