Folding transition of the triangular lattice.

We study the problem of folding of the regular triangular lattice in the presence of bending rigidity K and magnetic field h (conjugate to the local normal vectors to the triangles). A numerical study of the transfer matrix of the problem shows the existence of three first order transition lines in the (K, h) plane separating three phases: a folded phase, a phase frozen in the completely flat configuration (with all normal vectors pointing up) and its mirror image (all normal vectors pointing down). At zero magnetic field, a first order folding transition is found at a positive value Kc ≃ 0.11(1) of the bending rigidity, corresponding to a triple point in the phase diagram.