Fluctuation induced attraction between adhesion sites of supported membranes

We use scaling arguments and coarse grained Monte Carlo simulations to study the fluctuation mediated interactions between a pair of adhesion sites of a bilayer membrane and a supporting surface. We find that the potential of mean force is an infinitely long range attractive potential that grows logarithmically with the pair distance $r$: $\phi(\vec{r})/k_BT=c\ln r$, where the constant $c=2$ and $c=1$ for non-stressed and stressed membranes, respectively. When, in addition to excluded volume repulsion, the membrane also interacts with the underlying surface through a height-dependent attractive potential, the potential $\phi(\vec{r})$ is screened at large pair distances.