  We present the partition function of a most generic $U(N)$ single plaquette
model in terms of representations of unitary group. Extremising the partition
function in large N limit we obtain a relation between eigenvalues of unitary
matrices and number of boxes in the most dominant Young tableaux distribution.
Since, eigenvalues of unitary matrices behave like coordinates of free fermions
whereas, number of boxes in a row is like conjugate momenta of the same, a
relation between them allows us to provide a phase space distribution for
different phases of the unitary model under consideration. This proves a
universal feature that all the phases of a generic unitary matrix model can be
described in terms of topology of free fermi phase space distribution. Finally,
using this result and analytic properties of resolvent that satisfy
Dyson-Schwinger equation, we present a phase space distribution of unfolded
zeros of Riemann zeta function.
