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The Ginzburg-Landau (GL) equations for a d-wave superconductor are derivedwithin the context of two microscopic lattice models used to describe thecuprates: the extended Hubbard model and the Antiferromagnetic-van Hove model.Both models have pairing on nearest-neighbour links, consistent with theoriesfor d-wave superconductivity mediated by spin fluctuations. Analytical resultsobtained for the extended Hubbard model at low electron densities andweak-coupling are compared to results reported previously for a d-wavesuperconductor in the continuum. The variation of the coefficients in the GLequations with carrier density, temperature, and coupling constants arecalculated numerically for both models. The relative importance of anisotropichigher-order terms in the GL free energy is investigated, and the implicationsfor experimental observations of the vortex lattice are considered.Comment: ReVTeX, 18 pages, 7 postscript figures. To appear in Phys. Rev. B  (Jan. 1, 1997

Microscopic derivation of the Ginzburg-Landau equations for a d-wave superconductor