Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Statistical physics of complex networks II
DY 22.7: Talk
Wednesday, February 27, 2008, 18:15–18:30, MA 004
Spin Dynamics on Complex Networks — Filippo Radicchi1, Yong-Yeol Ahn2, and •Hildegard Meyer-Ortmanns3 — 1CNNL., ISI Foundation, 10133 Torino, Italy — 2Korea Adv.Inst.Science and Technology, Daejeon 305-701, Korea — 3SES, Jacobs University, 28725 Bremen, Germany
In the first part we consider Ising spin dynamics as it can be used to describe the approach to a state of social balance. We shall map this dynamics along with the associated algorithm to the process of solving a satisfiability problem of computer science. The network is varied from an all-to-all topology, to a random one with different degrees of dilution, and to regular topologies. As it turns out, the stationary states and the time of finding a solution depend on the topology as well as on the dilution parameter and the propensity parameter which characterizes the tendency to reduce frustration in the system. Even if an optimal solution exists it depends on the parameter choice whether the local stochastic algorithm is able to find it. In the second part we systematically interpolate between synchronous and asynchronous update of a chain of Ising spins. As a function of the interpolation parameter we identify a phase transition between the stationary states that belongs to the universality class of parity conservation. For fully synchronous update of the ferromagnetic Ising chain the stationary state becomes antiferromagnetic. Moreover, strongly asynchronous update for Boolean threshold dynamics considerably changes the phase space that is supposed to model the yeast cell cycle.