Weak first-order superfluid--solid quantum phase transitions
  We study superfluid--solid zero-temperature transitions in two-dimensional lattice boson/spin models by Worm-Algorithm Monte Carlo simulations. We observe that such transitions are typically first-order with the exception of special high-symmetry points which require fine tuning in the Hamiltonian parameter space. We present evidence that the superfluid--checkerboard solid and superfluid--valence-bond solid transitions at half-integer filling factor are extremely weak first-order transitions and in small systems they may be confused with continuous or high-symmetry points. 
Anatoly Kuklov, Nikolay Prokof'ev, and Boris Svistunov