Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coup
ling is to a weak first order transition, similar to the case of U(1)$times$U(1) symmetry. Our results imply that recent numeric studies of the N`{e}el antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
On the basis of first-principle Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp He4 crystal features a superfluid core. This is the first example of a regular quasi-one-dimensional supersolid, and one of
the cleanest cases of a regular Luttinger-liquid system. In contrast, the same type of screw dislocation in solid Hydrogen is insulating.
