  We study two-color lattice QCD with massless staggered fermions in the strong
coupling limit using a new and efficient cluster algorithm. We focus on the
phase diagram of the model as a function of temperature $T$ and baryon chemical
potential $\mu$ by working on $L_t \times L^d$ lattices in both $d=2,3$. In
$d=3$ we find that at $\mu=0$ the ground state of the system breaks the global
U(2) symmetry present in the model to U(1), while the finite temperature phase
transition (with $L_t=4$) which restores the symmetry is a weak first order
transition. In $d=2$ we find evidence for a novel phase transition similar to
the Berezinky-Kosterlitz-Thouless phenomena. On the other hand the quantum
(T=0) phase transition to a symmetric phase as a function of $\mu$ is second
order in both $d=2,3$ and belongs to the mean field universality class.
