  We report a numerical evidence of the discontinuous transition of a tethered
membrane model which is defined within a framework of the membrane elasticity
of Helfrich. Two kinds of phantom tethered membrane models are studied via the
canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of
spherical topology. A surface model is defined by the Gaussian term and the
bending energy term, and the other, which is tensionless, is defined by the
bending energy term and a hard wall potential. The bending energy is defined by
using the normal vector at each vertex. Both of the models undergo the
first-order phase transition characterized by a gap of the bending energy. The
phase structure of the models depends on the choice of discrete bending energy.
