  We study a two-dimensional fluid of dipolar hard disks by Monte Carlo
simulations in a square with periodic boundary conditions and on the surface of
a sphere. The theory of the dielectric constant and the asymptotic behaviour of
the equilibrium pair correlation function in the fluid phase is derived for
both geometries. After having established the equivalence of the two methods we
study the stability of the liquid phase in the canonical ensemble. We give
evidence of a phase made of living polymers at low temperatures and provide a
tentative phase diagram.
