  A \emph{monopole liquid} is a magnetic charge-disordered spin system defined
over an Ising pyrochlore lattice, with one single topological charge or
\emph{monopole} in each tetrahedron. We define a simple model Hamiltonian for
this system and compare its thermodynamics at zero magnetic field with that of
spin ice ---a phase free of these charges. In spite of the liquid-like
correlations between charges, we find that spins in the charged phase are
uncorrelated at all temperatures, like in a perfect paramagnet. The addition of
nearest neighbors interactions favoring neutral `2in-2out' excitations as a
perturbation has a peculiar effect. While they decrease charge-charge
correlations, new spin correlations resembling those in spin ice appear on
increasing temperature. This helps us understand why dipolar correlations are
observed in spin ices at unexpectedly high temperatures, and the major role of
double excitations in erasing the Coulomb phase correlations. Ferromagnetic
interactions strengthen the charges short range order and its associated spin
correlations. Finally, we discuss how the monopole liquid can be related to
other systems and materials where different phases of \emph{monopole matter}
have been observed.
