Publication : t94/073

Abstract:
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 $K_c\simeq 0.11(1)$ of the bending rigidity, corresponding to a triple point in the phase diagram.

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