FOLDING OF THE TRIANGULAR LATTICE WITH QUENCHED RANDOM BENDING RIGIDITY

We study the problem of folding of the regular triangular lattice in t he presence of a quenched random bending rigidity +/-K and a magnetic held h (conjugate to the local normal vectors to the triangles). The r andomness in the bending energy can be understood as arising from a pr ior marking of the lattice with quenched creases on which folds are fa vored. We consider three types of quenched randomness: (i) a ''physica l'' randomness where the creases arise from some prior random folding; (ii) a Mattis-like randomness where creases are domain walls of some quenched spin system; (iii) an Edwards-Anderson-like randomness where the bending energy is +/-K at random, independently on each bond. The corresponding (K,h) phase diagrams are determined in the hexagon appro ximation of the cluster variation method. Depending on the type of ran domness, the system shows essentially different behaviors.