The flat phase of fixed-connectivity membranes

Abstract

The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system \cite{BCFTA}. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.

7 pages, 5 figures, 3 tables. LaTeX w/epscrc2.sty, combined contribution of M. Falcioni and M. Bowick to LATTICE96(gravity), to appear in Nucl. Phys. B (proc. suppl.)

References in corpus (3)

• Self-Consistent Theory of Polymerized Membranes
• The Flat Phase of Crystalline Membranes
• The Critical Exponents of Crystalline Random Surfaces

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• First-order phase transition in the tethered surface model on a sphere
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• First-order phase transition of fixed connectivity surfaces
• Buckling of thermalized elastic sheets
• First-order phase transition of the tethered membrane model on spherical surfaces
• Phase transitions of a tethered membrane model on a torus with intrinsic curvature
• Phase transitions of a tethered surface model with a deficit angle term
• Monte Carlo simulations of a tethered membrane model on a disk with intrinsic curvature
• Nonvanishing string tension of elastic membrane models
• Improved Algorithms for Simulating Crystalline Membranes
• Phase structure of a surface model on dynamically triangulated spheres with elastic skeletons
• Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
• Phase transition of an extrinsic curvature model on tori