  The far infrared physics is a fascinating topic for theoretical physics,
since the foundation of quantum field theory and neutrinos seem to be strongly
related with the far infrared physics of our Universe. In this work we shall
explore the possibility of a late-time thermal phase transition caused by the
axion-neutrino interactions. The axion is assumed to be the misalignment axion
which is coupled primordially to a chiral symmetric neutrino. The chiral
symmetry is supposed to be broken either spontaneously or explicitly, and two
distinct phenomenological models of axion-neutrinos are constructed. The axion
behaves as cold dark matter during all its evolution eras, however if we assume
that the axion and the neutrino fields interact coherently in a classical way
as fields, or as ensembles, then we consider thermal effects in the axion
sector, due to the values of operators $\phi$ for the axion and $\bar{\nu}\nu$
due to the neutrinos. The thermal equilibrium between the two has no effect to
the axion effective potential for a wide temperature range. As we show,
contrary to the existing literature, the axion never becomes destabilized due
to the finite temperature effects, however if axion-Higgs higher order
non-renormalizable operators are present in the Lagrangian, the axion potential
is destabilized in the temperature range $T\sim 0.1\,$MeV down to $T\sim
0.01\,$eV and a first order phase transition takes place. The initial axion
vacuum decays to the energetically more favorable axion vacuum, and the latter
decays to the Higgs vacuum which is more preferable. This late-time phase
transition might take place in the redshift range $z\sim 385-37$ and thus it
may cause density fluctuations in the post-recombination era.
