  We consider membranes adhered through specific receptor-ligand bonds. Thermal
undulations of the membrane induce effective interactions between adhesion
sites. We derive an upper bound to the free energy that is independent of
interaction details. To lowest order in a systematic expansion we obtain
two-body interactions which allow to map the free energy onto a lattice gas
with constant density. The induced interactions alone are not strong enough to
lead to a condensation of individual adhesion sites. A measure of the thermal
roughness is shown to depend on the inverse square root of the density of
adhesion sites, which is in good agreement with previous computer simulations.
