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

Quantum critical phenomena of unconventional superconductors: U(1) gauge model of link Cooper pair