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arXiv · 1410.2190

A positive temperature phase transition in random hypergraph 2-coloring

Victor Bapst·Amin Coja-Oghlan·Felicia Raßmann
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Abstract

Diluted mean-field models are graphical models in which the geometry of interactions is determined by a sparse random graph or hypergraph. Based on a nonrigorous but analytic approach called the "cavity method", physicists have predicted that in many diluted mean-field models a phase transition occurs as the inverse temperature grows from $0$ to $\infty$ [Proc. National Academy of Sciences 104 (2007) 10318-10323]. In this paper, we establish the existence and asymptotic location of this so-called condensation phase transition in the random hypergraph $2$-coloring problem.

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Victor Bapst, Amin Coja-Oghlan, Felicia Raßmann. 2016-06-22. A positive temperature phase transition in random hypergraph 2-coloring. https://doi.org/10.1214/15-aap1119

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