Folding transition of the triangular lattice

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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Philippe Di Francesco, Emmanuel Guitter. Folding transition of the triangular lattice. Physical Review E , American Physical Society (APS), 1994, 50 (6), pp.4418-4426. ⟨10.1103/PhysRevE.50.4418⟩. ⟨cea-02009477⟩

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