  We study the moduli space of 4d N=1 supersymmetric QCD in the Veneziano limit
using Hilbert series. In this limit, the numbers of colours and flavours are
taken to be large with their ratio fixed. It is shown that the Hilbert series,
which is a partition function of an ensemble of gauge invariant quantities
parametrising the moduli space, can also be realised as a partition function of
a system of interacting Coulomb gas in two dimensions. In the electrostatic
equilibrium, exact and asymptotic analyses reveal that such a system exhibits
two possible phases. Physical quantities, such as charge densities, free
energies, and Hilbert series, associated with each phase, are computed
explicitly and discussed in detail. We then demonstrate the existence of the
third order phase transition in this system.
