We study thermodynamics of strongly coupled lattice QCD with two colors of massless staggered fermions as a function of the baryon chemical potential μ in 3+1 dimensions using a new cluster algorithm. We find evidence that the model undergoes a weak first order phase transition at μ=0 which becomes second order at a finite μ. Symmetry considerations suggest that the universality class of these phase transitions should be governed by a O(N)×O(2) field theory with collinear order, with N=3 at μ=0 and N=2 at μ≠0. The universality class of the second order phase transition at μ≠0 appears to be governed by the decoupled XY fixed point present in the O(2)×O(2) field theory. Finally we show that the quantum (T=0) phase transition as a function of μ is a second order mean field transition. © 2006 The American Physical Society.