The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q Abstract We study the phase diagram of the ferromagnetic q-state Potts model on the various three-dimensional lattices for integer and non-integer values of q > 1. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike approximation for the two-point correlation functions. We...

Recent progress in experiments on trapped ultracold atoms has made it possible to study the interplay between magnetism and superfluid-insulator transitions in the boson Hubbard model. We report on quantum Monte Carlo simulations of the spin-1 boson Hubbard model in the ground state. For antiferromagnetic interactions favoring singlets, we present exact numerical evidence that the superfluid-in...