  Critical phenomena arise ubiquitously in various context of physics, from
condensed matter, high energy physics, cosmology, to biological systems, and
consist of slow and long-distance fluctuations near a phase transition or
critical point. Usually, these phenomena are associated with the softening of a
massive mode. Here we show that a novel, non-Hermitian-induced mechanism of
critical phenomena that do not fall into this class can arise in the steady
state of generic driven-dissipative many-body systems with coupled binary order
parameters such as exciton-polariton condensates and driven-dissipative
Bose-Einstein condensates in a double-well potential. The criticality of this
``critical exceptional point'' is attributed to the coalescence of the
collective eigenmodes that convert all the thermal-and-dissipative-noise
activated fluctuations to the Goldstone mode, leading to anomalously giant
phase fluctuations that diverge at spatial dimensions $d\le 4$. Our dynamic
renormalization group analysis shows that this gives rise to a strong-coupling
fixed point at dimensions as high as $d<8$ associated with a new universality
class beyond the classification by Hohenberg and Halperin, indicating how
anomalously strong the many-body corrections are at this point. We find that
this anomalous enhancement of many-body correlation is due to the appearance of
a sound mode at the critical exceptional point despite the system's dissipative
character.
