  In this paper $4$ dimensional Riemannian (or Euclidean) vacuum general
relativity is recovered from a phase transition by spontaneous symmetry
breaking within a quantum field theory (all in the sense of the algebraic
approach) provided by the unique ${\rm II}_1$ hyperfinite factor von Neumann
algebra. The formal temperature of this phase transition is
$T=\frac{1}{2}T_{\rm Planck}\approx7.06\times 10^{31}{\rm K}$.
