We consider reversible, conservative Ginzburg-Landau processes, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433-499), we prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L-2. © 2002 Éditions scientifiques et médicales Elsevier SAS.