Possible types of critical behaviour and the mean size of dynamically triangulated random surfaces

A discretization of the bosonic string through dynamically triangulated surfaces with weights depending on the internal curvature is studied analytically and by Monte Carlo simulations. Special attention is paid to the mean square extent of the surfaces with given area. The model is shown to exist in three (possibly four) different phases depending on the dimension D of the embedding space and the value of the constant α coupled to the intrinsic curvature.