Phase transition in a U(1)-lattice-gauge system derived from a weakly three-dimensional t-J model

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 L3 lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size L2. Monte Carlo simulations are done on 123, 203, and 303 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 Tc decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below Tc, are also presented