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We propose a finite temperature Landau theory that describes competing ordersand interlayer tunneling in cuprate superconductors as an important extensionto a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)],where the superconducting transition temperature $T_c$ is defined in threepossible ways as a function of the zero temperature order parameter. For givenparameters, our theory determines $T_c$ without any ambiguity. In mono- anddouble-layer systems we discuss the relation between zero temperature orderparameter and the associated transition temperature in the presence ofcompeting orders, and draw a connection to the puzzling experimental fact thatthe pseudo-gap temperature is much higher than the corresponding energy scalenear optimum doping. Applying the theory to multi-layer systems, we calculatethe layer-number dependence of $T_c$. In a reasonable parameter space theresult turns out to be in agreement with experiments.Comment: 5 pages, 3 figure

Competing orders and interlayer tunneling in cuprate superconductors: A finite-temperature Landau theory