dorsal/arxiv
View SchemaReducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem
| Authors | Filippo Radicchi, Daniele Vilone, Sooeyon Yoon, Hildegard Meyer-Ortmanns |
|---|---|
| Categories | |
| ArXiv ID | physics/0608031 |
| URL | https://arxiv.org/abs/physics/0608031 |
| DOI | 10.1103/PhysRevE.75.026106 |
| Journal | Phys. Rev. E 75, 026106 (2007) |
Abstract
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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"abstract": "Reduction of frustration was the driving force in an approach to social\nbalance as it was recently considered by Antal \\emph{et al.} [ T. Antal, P. L.\nKrapivsky, and S. Redner, Phys. Rev. E {\\bf 72}, 036121 (2005). ]. We\ngeneralize their triad dynamics to $k$-cycle dynamics for arbitrary integer\n$k$. We derive the phase structure, determine the stationary solutions and\ncalculate the time it takes to reach a frozen state. The main difference in the\nphase structure as a function of $k$ is related to $k$ being even or odd. As a\nsecond generalization we dilute the all-to-all coupling as considered by Antal\n\\emph{et al.} to a random network with connection probability $w\u003c1$. ...",
"arxiv_id": "physics/0608031",
"authors": [
"Filippo Radicchi",
"Daniele Vilone",
"Sooeyon Yoon",
"Hildegard Meyer-Ortmanns"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1103/PhysRevE.75.026106",
"journal_ref": "Phys. Rev. E 75, 026106 (2007)",
"title": "Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem",
"url": "https://arxiv.org/abs/physics/0608031"
},
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