  We explore the phase diagram of two-component bosons with Feshbach resonant
pairing interactions in an optical lattice. It has been shown in previous work
to exhibit a rich variety of phases and phase transitions, including a
paradigmatic Ising quantum phase transition within the second Mott lobe. We
discuss the evolution of the phase diagram with system parameters and relate
this to the predictions of Landau theory. We extend our exact diagonalization
studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising
critical exponents for the longitudinal and transverse magnetic
susceptibilities within the second Mott lobe. The numerical results for the
ground state energy and transverse magnetization are in good agreement with
exact solutions of the Ising model in the thermodynamic limit. We also provide
details of the low-energy spectrum, as well as density fluctuations and
superfluid fractions in the grand canonical ensemble.
