  The thermodynamic problem of a gas of static quarks carrying U(N) charges and
interacting with each other via U(N) electric gauge fields is formulated and
solved in the large N limit. In a lattice theory, the solution can be found in
any dimension. In particular, in 1+1-dimensions, the continuum model can also
be solved. In that case, and when the quarks are in the adjoint representation,
the explicit solution exhibits a first order quark confinement-deconfinement
transition at a critical temperature and density. We also show that, when there
are fundamental representation quarks, this phase transition persists until the
relative density of fundamental quarks is comparable to the density of adjoint
quarks, where it becomes a third order transition. We discuss the possible
interpretation of the third order transition as deconfinement.
