Thermal fluctuations and stiffening of heterogeneous fluid membranes

We study the effects of thermal fluctuations on symmetric tensionless heterogeneous (two-component) fluid membranes in a simple minimal model. Close to the critical point $T_c$ of the associated miscibility phase transition of the composition and for sufficiently strong curvature-composition interactions, mediated through a composition-dependent bending modulus, thermal fluctuations lead to enhancement of the effective bending modulus. Thus, the membrane conformation fluctuations will be {\em suppressed} near $T_c$, in comparison with a pure fluid membrane, for which thermal fluctuations are known to reduce the effective bending modulus at all non-zero temperatures.