Steiner Variations on Random Surfaces

TL;DR

This paper investigates modified Steiner actions for random surfaces, exploring their properties and numerical behavior, and compares them with established Gaussian and extrinsic curvature actions.

Contribution

It introduces and numerically analyzes Steiner variations, assessing their effectiveness and comparing them with traditional random surface actions.

Findings

Modified Steiner actions have potential but face issues with partition function convergence.

Adding an area term can improve the properties of Steiner-based actions.

Numerical results show differences in surface behavior between Steiner variations and traditional actions.

Abstract

Ambartzumian et.al. suggested that the modified Steiner action functional had desirable properties for a random surface action. However, Durhuus and Jonsson pointed out that such an action led to an ill-defined grand-canonical partition function and suggested that the addition of an area term might improve matters. In this paper we investigate this and other related actions numerically for dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.