Phases and fluctuations in a model for asymmetric inhomogeneous fluid membranes

We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase diagram displays either a first- or a second-order phase transition through a critical point (CP) or a tricritical point (TP), depending upon the bending modulus. It predicts generic nontrivial enhancement in fluctuations of asymmetric membranes that scales with system size in a power-law fashion at the CP and TP in two dimensions, not observed in symmetric membranes. It also yields two-dimensional Ising universality class for symmetric membranes, in agreement with experimental results.