A scale-free network hidden in the 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 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.

4 pages, 3 figures, address corrected

References in corpus (16)

• Statistical mechanics of complex networks
• Scale-Free Networks are Ultrasmall
• Sandpile on Scale-Free Networks
• Scale-free Networks from Optimal Design
• Networks and Cities: An Information Perspective
• The network topology of a potential energy landscape: A static scale-free network
• Ising model in small-world networks
• What is the length of a knot in a polymer?
• Growth Algorithms for Lattice Heteropolymers at Low Temperatures
• Equilibrium shapes of flat knots
• Scaling Properties of Random Walks on Small-World Networks
• Scale free networks from a Hamiltonian dynamics
• Peculiar scaling of self-avoiding walk contacts
• Self-avoiding walks and connective constants in small-world networks
• The traveling salesman problem, conformal invariance, and dense polymers
• Pseudoknots in a Homopolymer

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