On the Crumpling Transition in Crystalline Random Surfaces

TL;DR

This study analyzes the crumpling transition in crystalline random surfaces with extrinsic curvature, providing evidence for a second order phase transition and detailed critical exponents, with implications for understanding surface behavior.

Contribution

It offers the first detailed numerical analysis of the crumpling transition with extrinsic curvature on large lattices, confirming the transition's second order nature and precise critical exponents.

Findings

Transition is consistent with second order phase transition

Critical exponent for correlation length is approximately 0.89

Hausdorff dimension remains infinite in the crumpled phase

Abstract

We investigate the crumpling transition on crystalline random surfaces with extrinsic curvature on lattices up to $64^2$. Our data are consistent with a second order phase transition and we find correlation length critical exponent $\nu=0.89\pm 0.07$. The specific heat exponent, $\alpha=0.2\pm 0.15$, is in much better agreement with hyperscaling than hitherto. The long distance behaviour of tangent-tangent correlation functions confirms that the so-called Hausdorff dimension is $d_H=\infty$ throughout the crumpled phase.