Folding transition of the triangular lattice

Philippe Di Francesco (1) , Emmanuel Guitter (1)

1 SPhT - Service de Physique Théorique

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.

Domains: Physics [physics]

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