Global Mode Coupling and Environmental Modulation in a Ginzburg–Landau Field Theory

We study a minimal extension of the Ginzburg–Landau framework incorporating a global quadratic coupling of the order parameter and a slowly varying environmental modulation field. The global term introduces a non-local interaction acting exclusively on the zero-momentum sector, while the environmental field modulates the local effective mass. We show at the Gaussian (quadratic) level that the model leads to:(i) a finite-size dependent shift of the homogeneous mode mass,(ii) suppression of infrared fluctuations in the zero-momentum sector, and(iii) separation between homogeneous and finite-momentum fluctuations.The model remains analytically tractable and reduces to standard Ginzburg–Landau theory in the limit of vanishing global coupling.