Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem

Details Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem Long Range Frustrations in a Spin Glass Model of the Vertex Cover Problem

2004-11-03

arxiv.org/abs/cond-mat/0411077v3

Physical Review Letters 94, 217203 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Final version as appeared in PRL

Scientific paper

10.1103/PhysRevLett.94.217203

In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain combinations of spin values for these vertices may never appear in any configuration of this domain. We present a mean field theory to tackle such long range frustrations and apply it to the NP--hard minimum vertex cover (hard--core gas condensation) problem. Our analytical results on the ground--state energy density and on the fraction of frozen vertices are in good agreement with known numerical and mathematical results.

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