Phase diagram of two-color lattice QCD in the chiral limit

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.Comment: 31 pages, 12 figure