Extrinsic curvature in dynamically triangulated random surface models

The phase structure of a dynamically triangulated random surface model, the action containing extrinsic curvature, is investigated using Monte Carlo techniques. Our simulations are carried out in D=3 and compare the behaviour of the model for two different forms of the discrete curvature term. With the first, essentially (δX)², we observe a third order transition near β≈0.7, where β is the associated coupling. The phase structure of the model with the second type, Σ(1-cosθ_ij) proves markedly different, a strong second order phase transition is presented at finite β, leading to the possibility of a new continuum limit for the model. We discuss the implications of these results for continuum surfaces.