1308.0255 (Chung-Pin Chou et al.)

Order-disorder duality of second order phase transitions: The topology
of complex networks    [PDF]

Chung-Pin Chou, Ming-Chiang Chung

Many networks of interests in the real world, such as social networks, computer networks and biological networks, have been widely studied by using network analysis tools. In this letter we use these techniques to study phase transitions in one-dimensional quantum Ising model and two-dimensional classical XY model. We demonstrate that whereas the phase in real space is transited from an ordered to a disordered state, the network topology surprisingly changes from a disordered to an ordered state. We call this correspondence as "order-disorder duality". Several network quantities, e.g., global efficiency, clustering coefficient and small-worldness, can play similar roles as order parameters in Landau symmetry-breaking theory. We suggest that the network measurements originating from topological network structures can provide useful tools to characterize the phase transitions in any given model. In addition, we discuss the possibility of the small-world property in these two models.

View original: http://arxiv.org/abs/1308.0255