Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem

Details Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem

2006-08-03

arxiv.org/abs/physics/0608031v1

Phys. Rev. E 75, 026106 (2007)

Physics

Physics and Society

20 pages, 14 figures. Submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.75.026106

Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal \emph{et al.} [ T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005). ]. We generalize their triad dynamics to $k$-cycle dynamics for arbitrary integer $k$. We derive the phase structure, determine the stationary solutions and calculate the time it takes to reach a frozen state. The main difference in the phase structure as a function of $k$ is related to $k$ being even or odd. As a second generalization we dilute the all-to-all coupling as considered by Antal \emph{et al.} to a random network with connection probability $w<1$. ...

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