A Polymerized Membrane in Confined Geometry

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Abstract
The fluctuations of a self-avoiding, polymerized (or tethered) membrane which is restricted by the presence of two parallel hard walls are studied using Monte Carlo simulations and scaling arguments. The universal exponent which characterizes the X-ray scattering intensity of lamellar systems in the decoupled phase is determined and the renormalized bending rigidity is obtained from the mean curvature susceptibility. Our results are consistent with an exponent η 0.60 ± 0.10. We also determine for the first time the critical exponent which characterizes curvature fluctuations near the membrane's edge.