Quantum phase transition of infrared radiation

We describe a phase transition of infrared radiation, driven by quantum fluctuations, which takes place at the boundary of (the conformal diagram of) Minkowski spacetime. Specifically, we consider a family of states interpolating between the vacuum and the Kraus-Polley-Reents infravacuum. A state from this family can be imagined as a static source emitting flashes of infrared radiation in distant past. The flashes are in suitable squeezed states and the time intervals between them are controlled by a certain parameter r. For r<0 the states are lightcone normal, thus physically indistinguishable from local excitations of the vacuum. They suffer from the usual infrared problems such as disintegration of the Bloch-Nordsieck S-matrix and rotational symmetry breaking by soft photon clouds. However, for r>0 lightcone normality breaks down, the S-matrix is stabilized by the Kraus-Polley-Reents mechanism and the rotational symmetry is restored. We interpret these two situations as ordered (r<0) and disordered (r>0) phase of infrared radiation, and show that they can be distinguished by asymptotic fluctuations of the fields. We also determine the singular behaviour of some S-matrix elements near the critical point r=0.