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Abstract: We investigate a Hamiltonian model of networks. The model is a mirrorformulation of the XY model hence the name - instead letting the XY spinsvary, keeping the coupling topology static, we keep the spins conserved andsample different underlying networks. Our numerical simulations show complexscaling behaviors, but no finite-temperature critical behavior. The groundstate and low-order excitations for sparse, finite graphs is a fragmented setof isolated network clusters. Configurations of higher energy are typicallymore connected. The connected networks of lowest energy are stretched outgiving the network large average distances. For the finite sizes we investigatethere are three regions - a low-energy regime of fragmented networks, andintermediate regime of stretched-out networks, and a high-energy regime ofcompact, disordered topologies. Scaling up the system size, the borders betweenthese regimes approach zero temperature algebraically, but different networkstructural quantities approach their T=0-values with different exponents.

Autor: Petter Holme, Zhi-Xi Wu, Petter Minnhagen


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