We show that lateral fluidity in membranes containing quenched protein
obstacles belongs to the universality class of the two-dimensional random-field
Ising model. The main feature of this class is the absence of a phase
transition: there is no critical point, and macroscopic domain formation does
not occur. Instead, there is only one phase. This phase is highly
heterogeneous, with a structure consisting of micro-domains. The presence of
quenched protein obstacles thus provides a mechanism to stabilize lipid rafts
in equilibrium. Crucial for two-dimensional random-field Ising universality is
that the obstacles are randomly distributed, and have a preferred affinity to
one of the lipid species. When these conditions are not met, standard Ising or
diluted Ising universality apply. In these cases, a critical point does exist,
marking the onset toward macroscopic demixing.Comment: 10 pages, 10 figure
