The Critical Exponents of Crystalline Random Surfaces

Abstract

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be $\nu =0.71(5)$ from the tangent-tangent correlation function whereas we find $\nu =0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $\alpha =0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a ${\chi }^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $\alpha$. Our measurements of the normal-normal correlation functions suggest that the model in the crumpled phase is described by an effective field theory which deviates from a free field theory only by super-renormalizable interactions.

18 pages standard LaTex with EPS figures

References in corpus (1)

• On the Crumpling Transition in Crystalline Random Surfaces

Cited by in corpus (28)

• The Statistical Mechanics of Membranes
• First-order transition of tethered membranes in 3d space
• First-order phase transition in the tethered surface model on a sphere
• Nonlocal effective average action approach to crystalline phantom membranes
• First-order phase transition of fixed connectivity surfaces
• Thermal crumpling of perforated two-dimensional sheets
• The flat phase of fixed-connectivity membranes
• First-order phase transition of the tethered membrane model on spherical surfaces
• Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Grand Canonical simulations of string tension in elastic surface model
• 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
• Phase transition of surface models with intrinsic curvature
• 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
• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
• Shape transformations of a compartmentalized fluid surface
• Phase structure of a surface model on dynamically triangulated spheres with elastic skeletons
• Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
• Phase structure of intrinsic curvature models on dynamically triangulated disk with fixed boundary length
• Phase transitions in a fluid surface model with a deficit angle term
• Numerical simulation of random paths with a curvature dependent action
• Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
• Phase transition of an extrinsic curvature model on tori
• Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries