  In this paper we shall study quantum critical behavior of lattice model of
unconventional superconductors (SC) that was proposed in the previous papers.
In this model, the Cooper-pair (CP) field is defined on lattice links in order
to describe d-wave SC. The CP field can be regarded as a U(1) lattice gauge
field, and the SC phase transition takes place as a result of the phase
coherence of the CP field. Effects of the long-range Coulomb interactions
between the CP's and fluctuations of the electromagnetic field are taken into
account. We investigate the phase structure of the model and the critical
behavior by means of the Monte Carlo simulations. We find that the parameter,
which controls the fluxes (vortices) of the CP, strongly influences the phase
structure. In three-dimensional case, the model has rich phase structure. In
particular there is a "monopole proliferation" phase transition besides the SC
phase transition. Depending on the parameters, this transition exists within
the SC phase or takes place simultaneously with the SC transition. This new
type of transition is relevant for unconventional SC's with strong spatial
three-dimensionality and to be observed by experiments.
