Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem
<|reference_start|>Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem: 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.<|reference_end|>
@article{zhou2004long,
    title={Long range frustration in finite connectivity spin glasses: A mean field
  theory and its application to the random $K$-satisfiability problem},
    author={Haijun Zhou},
    journal={New Journal of Physics 7: 123 (2005)},
    year={2004},
    doi={10.1088/1367-2630/7/1/123},
    archivePrefix={arXiv},
    eprint={cond-mat/0411079},
    primaryClass={cond-mat.dis-nn cond-mat.stat-mech cs.CC}
}