Microcanonical simulations of randomly triangulated planar random surfaces

Results of Monte Carlo simulations of a model of random surfaces based on planar random triangulations with gaussian embedding in d-dimensional euclidean space are presented for various positive and negative values of d. The fractal dimension (Hausdorff dimension of the embedding) is large and decreases slightly with d. The spreading dimension (intrinsic Hausdorff dimension of the random lattice) is greater than two and increases with d. Flat regular lattices dominate at large negative d and very irregular ones for large positive d. There is a significant linear correlation between the effective action and the discrete Liouville action. (orig.)