Publication : t96/083

Abstract:
We study the problem of folding of the regular triangular lattice in the presence of a quenched random bending rigidity $\pm K$ and a magnetic field $h$ (conjugate to the local normal vectors to the triangles). The randomness in the bending energy can be understood as arising from a prior marking of the lattice with quenched creases on which folds are favored. We consider three types of quenched randomness: (1) a ``physical'' randomness where the creases arise from some prior random folding; (2) a Mattis-like randomness where creases are domain walls of some quenched spin system; (3) an Edwards-Anderson-like randomness where the bending energy is $\pm K$ at random independently on each bond. The corresponding $(K,h)$ phase diagrams are determined in the hexagon approximation of the cluster variation method. Depending on the type of randomness, the system shows essentially different behaviors.

publi.pdf