Abstract
A lattice model of random surfaces is studied including configurations with arbitrary topologies, overhangs and bubbles. The Hamiltonian of the surface includes a term proportional to its area and a scale-invariant integral of the squared mean curvature. We propose a discretization of the curvature which ensures the scale-invariance of the bending energy on the lattice. Nonperturbative renormalization groups for the surface tension and the bending rigidity are applied, which are also valid at high temperatures and scales above the persistence length. We find at vanishing surface tensions a closed expression for the scale dependent rigidity including the usual logarithmic decay at low temperatures. Different scaling behaviours at non-vanishing tensions occur yielding characteristic length scales, which determine the structure of homogeneous droplet, lamellar, and microemulsion phases.
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References
Gompper, G. and Schick, M.: Self-assembling amphiphilic systems. In: Phase Transitions and Critical Phenomena', Vol. 16, Domb, C., Lebowitz, J. (eds.) London: Academic Press 1994
Helfrich, W.: J. Phys. (Paris)46, 1263 (1985):48, 285 (1987)
Peliti, W., Leibler, S.: Phys. Rev. Lett.54, 1690 (1985)
Förster, D.: Phys. Lett. A114, 115 (1986)
Kleinert, H.: Phys. Lett. A114, 263 (1986)
David, F., Leibler, S.: J. Phys. II (France)1, 959 (1991)
Burkhardt, T.W., van Leuwen, J.M.J.: Real Space Renormalization. Berlin: Springer 1982
Domb, C., Green, M.S. (eds.) Phase Transitions and Critical Phenomena', vol. 6. London: Academic Press 1976
Helfrich, W.: Z. Naturforsch,28c, 693 (1973)
Santaló, L.A.: Integral Geometry and Geometric Probability. Reading, Mass: Addison-Wesley 1976
Mecke, K.R. Integralgeometrie in der Statistischen Physik. Harri-Deutsch 1994