THE THEORY OF DYNAMICAL RANDOM SURFACES WITH EXTRINSIC CURVATURE
J. Ambj{\o}rn, A. Irb\"ack, J. Jurkiewicz and B. Petersson
Abstract: We analyze numerically the critical properties of a two-
dimensional discretized random surface with extrinsic curvature
embedded in a three-dimensional space. The use of the toroidal topology
enables us to enforce the non-zero external extension without the
necessity of defining a boundary and allows us to measure directly
the string tension. We show that a phase transition from the crumpled
phase to the smooth phase observed earlier for a spherical topology
appears also for a toroidal surface for the same finite value of the
coupling constant of the extrinsic curvature term. The phase transition
is characterized by the vanishing of the string tension. We discuss the
possible non-trivial continuum limit of the theory, when approaching
the critical point. Numerically we find the value of the critical
exponent $\nu$ to be between 0.38 and 0.42. The specific heat, related
to the extrinsic curvature term, seems not to diverge (or diverge slower
than logarithmically) at the critical point.