  Motivated by the still ongoing debate about the various possible meanings of
the term surface tension of bilayer membranes, we present here a detailed
discussion that explains the differences between the "intrinsic",
"renormalized", and "mechanical" tensions. We use analytical considerations and
computer simulations to show that the membrane spectrum of thermal fluctuations
is governed by the mechanical and not the intrinsic tension. Our study
highlights the fact that the commonly used quadratic approximation of Helfrich
effective Hamiltonian is not rotationally invariant. We demonstrate that this
non-physical feature leads to a calculated mechanical tension that differs
dramatically from the correct mechanical tension. Specifically, our results
suggest that the mechanical and intrinsic tensions vanish simultaneously, which
contradicts recent theoretical predictions derived for the approximated
Hamiltonian.
