Fluid Random Surfaces with Extrinsic Curvature: II

TL;DR

This paper extends previous simulations of random surfaces with extrinsic curvature, showing that the specific heat peak stabilizes with larger lattices and providing insights into the nature of the crumpling transition.

Contribution

It presents new large-scale simulation results that analyze the behavior of extrinsic curvature in random surfaces, offering evidence about the crumpling transition and finite-size effects.

Findings

The specific heat peak ceases to grow on lattices larger than 576 nodes.

The peak's location stabilizes with increasing lattice size.

Evidence for a true crumpling transition remains weak.

Abstract

We present the results of an extension of our previous work on large-scale simulations of dynamically triangulated toroidal random surfaces embedded in $R^3$ with extrinsic curvature. We find that the extrinsic-curvature specific heat peak ceases to grow on lattices with more than 576 nodes and that the location of the peak $\lam_c$ also stabilizes. The evidence for a true crumpling transition is still weak. If we assume it exists we can say that the finite-size scaling exponent $\frac {\alpha} {\nu d}$ is very close to zero or negative. On the other hand our new data does rule out the observed peak as being a finite-size artifact of the persistence length becoming comparable to the extent of the lattice.