CRITICAL PROPERTIES OF THE DYNAMICAL RANDOM SURFACE WITH EXTRINSIC
CURVATURE
J. Ambj{\o}rn, J. Jurkiewicz, S. Varsted, A. Irb\"ack 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 most probably second-order 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.