We numerically study a U(1)-lattice-gauge system, which is an effective model of the Ginzburg-Landau-type obtained from the t-J model of electrons. The model, which we call the ‘‘GL’’ model for short, is composed of link variables interpreted as a nearest-neighbor hole-pair field bounded by the singlet spin pairs. We concentrate our attention on the weakly three-dimensional case in which the electron hopping in the third direction is suppressed compared to other directions. When we simulate the model on an ${\mathit{L}}^3$ lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size ${\mathit{L}}^2$. Monte Carlo simulations are done on ${12}^3$, ${20}^3$, and ${30}^3$ lattices with the electron density slightly less than the half-filled one (the doping parameter δ is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature ${\mathit{T}}_{\mathit{c}}$ decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below ${\mathit{T}}_{\mathit{c}}$, are also presented.

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