Fluid membranes which experience interaction potentials with a potenti
al barrier are studied by Monte Carlo simulations. For a symmetric dou
ble-well potential, the membranes are found to exhibit the same critic
al behavior as the 2-dimensional Ising model even for zero lateral ten
sion. For an asymmetric adhesion potential with a relatively large pot
ential barrier, the unbound phase is found to nucleate via the formati
on of membrane 'islands' which implies a discontinuous unbinding trans
ition.