  Motivated by experiments on heteronuclear Feshbach resonances in Bose
mixtures, we investigate s-wave pairing of two species of bosons in an optical
lattice. The zero temperature phase diagram supports a rich array of superfluid
and Mott phases and a network of quantum critical points. This topology reveals
an underlying structure that is succinctly captured by a two-component Landau
theory. Within the second Mott lobe we establish a quantum phase transition
described by the paradigmatic longitudinal and transverse field Ising model.
This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We
also find this transition in the homonuclear case.
