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The anisotropic d=3 tJ model is studied by renormalization-group theory,yielding the evolution of the system as interplane coupling is varied from theisotropic three-dimensional to quasi-two-dimensional regimes.Finite-temperature phase diagrams, chemical potential shifts, and in-plane andinterplane kinetic energies and antiferromagnetic correlations are calculatedfor the entire range of electron densities. We find that the novel tau phase,seen in earlier studies of the isotropic d=3 tJ model, and potentiallycorresponding to the superconducting phase in high-T_c materials, persists evenfor strong anisotropy. While the tau phase appears at low temperatures at30-35% hole doping away from <n_i>=1, at smaller hole dopings we see a complexlamellar structure of antiferromagnetic and disordered regions, with asuppressed chemical potential shift, a possible marker of incommensurateordering in the form of microscopic stripes. An investigation of therenormalization-group flows for the isotropic two-dimensional tJ model alsoshows a pre-signature of the tau phase, which appears with finite transitiontemperatures upon addition of the smallest interplane coupling.Comment: 13 pages, 7 figures; replaced with published versio

d = 3 anisotropic and d = 2 tJ models: phase diagrams, thermodynamic properties, and chemical potential shift