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Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
Europhysics Letters
  • Wenjia Liu, Virginia Polytechnic Institute and State University
  • Beate Schmittmann, Iowa State University
  • R. K. P. Zia, Virginia Polytechnic Institute and State University
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Using Monte Carlo and analytic techniques, we study a minimal dynamic network involving two populations of nodes, characterized by different preferred degrees. Reminiscent of introverts and extroverts in a population, one set of nodes, labeledintroverts (I), prefers fewer contacts (a lower degree) than the other, labeled extroverts (E). As a starting point, we consider anextreme case, in which an I simply cuts one of its links at random when chosen for updating, while an E adds a link to a random unconnected individual (node). The model has only two control parameters, namely, the number of nodes in each group, NI and NE. In the steady state, only the number of crosslinks between the two groups fluctuates, with remarkable properties: Its average (X) remains very close to 0 for all NI > NE or near its maximum () if NI < NE. At the transition (NI = NE), the fraction wanders across a substantial part of [0,1], much like a pure random walk. Mapping this system to an Ising model with spin-flip dynamics and unusual long-range interactions, we note that such fluctuations are far greater than those displayed in either first- or second-order transitions of the latter. Thus, we refer to the case here as an "extraordinary transition". Thanks to the restoration of detailed balance and the existence of a "Hamiltonian", several qualitative aspects of these remarkable phenomena can be understood analytically.

This is an author's manuscript of an article from Europhysics Letters 100 (2012): 66007, doi:10.1209/0295-5075/100/66007.

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Wenjia Liu, Beate Schmittmann and R. K. P. Zia. "Extraordinary variability and sharp transitions in a maximally frustrated dynamic network" Europhysics Letters Vol. 100 Iss. 6 (2012) p. 66007
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