Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-11-03
New Journal of Physics 7: 123 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
Final version. Published in New Journal of Physics, freely available at http://www.njp.org/
Scientific paper
10.1088/1367-2630/7/1/123
Shortened abstract: A mean field theory of long range frustration is constructed for spin glass systems with quenched randomness of vertex--vertex connections and of spin--spin coupling strengths. This theory is applied to a spin glass model of the random $K$-satisfiability problem (K=2 or K=3). The zero--temperature phase diagram of the $\pm J$ Viana--Bray model is also determined, which is identical to that of the random 2-SAT problem. The predicted phase transition between a non-frustrated and a long--rangely frustrated spin glass phase might also be observable in real materials at a finite temperature.
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