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We study a model of a lipid bilayer membrane described by two orderparameters: the chemical composition described using the Gaussian model and thespatial configuration described with the elastic deformation model of amembrane with a finite thickness, or equivalently, for an adherent membrane. Weassume and explain on physical grounds the linear coupling between the twoorder parameters. Using the exact solution, we calculate the correlationfunctions and order parameters profiles. We also study the domains that formaround inclusions on the membrane. We propose and compare six distinct ways toquantify the size of such domains. Despite of its simplicity, the model hasmany interesting features like Fisher-Widom line or two distinct criticalregions.

Protein-lipid domains in heterogeneous membranes beyond spontaneous curvature effects