  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.
