  We found that three types of tethered surface model undergo a first-order
phase transition between the smooth and the crumpled phase. The first and the
third are discrete models of Helfrich, Polyakov, and Kleinert, and the second
is that of Nambu and Goto. These are curvature models for biological membranes
including artificial vesicles. The results obtained in this paper indicate that
the first-order phase transition is universal in the sense that the order of
the transition is independent of discretization of the Hamiltonian for the
tethered surface model.
