We address the problem of "phantom" folding of the tethered membrane modelled
by the two-dimensional square lattice, with bonds on the edges and diagonals of
each face. Introducing bending rigidities K1 and K2 for respectively long
and short bonds, we derive the complete phase diagram of the model, using
transfer matrix calculations. The latter displays two transition curves, one
corresponding to a first order (ferromagnetic) folding transition, and the
other to a continuous (anti-ferromagnetic) unfolding transition.Comment: TeX using harvmac.tex and epsf.tex, 22 pages (l mode), 17 figure
