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Theoretical models describing specific adhesion of membranes predict (forcertain parameters) a macroscopic phase separation of bonds into adhesiondomains. We show that this behavior is fundamentally altered if the membrane ispinned randomly due to, e.g., proteins that anchor the membrane to thecytoskeleton. Perturbations which locally restrict membrane height fluctuationsinduce quenched disorder of the random-field type. This rigorously prevents theformation of macroscopic adhesion domains following the Imry-Ma argument [Y.Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction ofrandom-field disorder follows from analytical calculations, and is strikinglyconfirmed in large-scale Monte Carlo simulations. These simulations are basedon an efficient composite Monte Carlo move, whereby membrane height and bonddegrees of freedom are updated simultaneously in a single move. The applicationof this move should prove rewarding for other systems also.

Random pinning limits the size of membrane adhesion domains