  We study thermodynamics of strongly coupled lattice QCD with two colors of
massless staggered fermions as a function of the baryon chemical potential
$\mu$ in 3+1 dimensions using a new cluster algorithm. We find evidence that
the model undergoes a weak first order phase transition at $\mu=0$ which
becomes second order at a finite $\mu$. Symmetry considerations suggest that
the universality class of these phase transitions should be governed by an
$O(N)\times O(2)$ field theory with collinear order, with N=3 at $\mu=0$ and
N=2 at $\mu \neq 0$. The universality class of the second order phase
transition at $\mu\neq 0$ appears to be governed by the decoupled XY fixed
point present in the $O(2)\times O(2)$ field theory. Finally we show that the
quantum (T=0) phase transition as a function of $\mu$ is a second order mean
field transition.
