  We examine the statistical mechanics of a 1-dimensional gas of both adjoint
and fundamental representation quarks which interact with each other through
1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when
the density of fundamental quarks is small, there is a first order phase
transition at a critical temperature and adjoint quark density which can be
interpreted as deconfinement. When the fundamental quark density is comparable
to the adjoint quark density, the phase transition becomes a third order one.
We formulate a way to distinguish the phases by considering the expectation
values of high winding number Polyakov loop operators.

High Energy Physics - Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology