  The adhesion of biological membranes is controlled by various types of
receptor and ligand molecules. In this letter, we present a
statistical-mechanical model for membranes that interact via receptor/ligand
bonds of two different lengths. We show that the equilibrium phase behavior of
the membranes is governed by an effective double-well potential. The depths of
the two potential wells depend on the concentrations and binding energies of
the receptors and ligands. The membranes are unbound for small, and bound for
larger potential depths. In the bound state, the length mismatch of the
receptor/ligand bonds can lead to lateral phase separation. We derive explicit
scaling laws for the critical points of unbinding and phase separation, and
determine the prefactors by comparison with Monte Carlo results.
