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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 transitionsdoi:10.1103/physrevlett.93.230402 pmid:15601129 fatcat:4hy2hixx25ehjir3xos5ls2m7e