  We consider the main transition in single-component membranes using computer
simulations of the Pink model [D. Pink {\it et al.}, Biochemistry {\bf 19}, 349
(1980)]. We first show that the accepted parameters of the Pink model yield a
main transition temperature that is systematically below experimental values.
This resolves an issue that was first pointed out by Corvera and co-workers
[Phys. Rev. E {\bf 47}, 696 (1993)]. In order to yield the correct transition
temperature, the strength of the van der Waals coupling in the Pink model must
be increased; by using finite-size scaling, a set of optimal values is
proposed. We also provide finite-size scaling evidence that the Pink model
belongs to the universality class of the two-dimensional Ising model. This
finding holds irrespective of the number of conformational states. Finally, we
address the main transition in the presence of quenched disorder, which may
arise in situations where the membrane is deposited on a rough support. In this
case, we observe a stable multi-domain structure of gel and fluid domains, and
the absence of a sharp transition in the thermodynamic limit.
