  We study the effects of the leading irrelevant perturbations on chiral
symmetry breaking in the effective $QED_3$ theory of d-wave
superconductor-insulator transition in underdoped cuprates. For weak symmetry
breaking, the effect of a perturbation on energies of various insulating states
can be classified according to its engineering dimension in the maximally
symmetric theory. Considering the velocity anisotropy, repulsive interactions,
and higher order derivatives we show that the insulating state with the lowest
energy is the spin density wave.
