Freezing a Fluid Random Surface

TL;DR

This paper explores how adding a curvature term to a random surface model can freeze the surface's geometry, transitioning it from fluid to crystalline states, and provides a new method to control surface regularity.

Contribution

It introduces a curvature-based term that interpolates between fluid and crystalline random surfaces, demonstrating how geometry can be stabilized by this modification.

Findings

Flips are frozen out as the curvature term coefficient increases.

The internal geometry becomes more regularized with higher curvature term.

The method offers a way to control the fluidity or crystallinity of random surfaces.

Abstract

We investigate a dynamically triangulated random surface action that consists of a gaussian term plus the modulus of the intrinsic scalar curvature. We find that the flips are frozen out and the internal geometry is regularized as the coefficient of the latter term is increased. Such a term thus provides a way of interpolating between dynamically triangulated (ie fluid) and crystalline random surfaces.