A positive temperature phase transition in random hypergraph 2-coloring

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.