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 ${\mathit{K}}_{\mathit{c}}$≃0.11(1) of the bending rigidity, corresponding to a triple point in the phase diagram.

• Received 14 June 1994

DOI:https://doi.org/10.1103/PhysRevE.50.4418