Steiner Variations on Random Surfaces

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. There has been considerable recent interest in the theory and simulation of random surfaces, inspired both by string theory and the study of membranes in solid state physics. The Polyakov partition function [1] for a string embedded in euclidean space with a fixed intrinsic area worldsheet discretizes to