FLUID RANDOM SURFACES WITH EXTRINSIC CURVATURE .2.

We present the results of an extension of our previous work on large-s cale simulations of dynamically triangulated toroidal random surfaces embedded in R3 with extrinsic curvature. We find that the extrinsic-cu rvature specific heat peak ceases to grow on lattices with more than 5 76 nodes and that the location of the peak lambda(c) also stabilizes. The evidence for a true crumpling transition is still weak. If we assu me it exists we can say that the finite-size scaling exponent alpha/nu d is very close to zero or negative. On the other hand our new data do es rule out the observed peak as being a finite-size artifact of the p ersistence length becoming comparable to the extent of the lattice.