FOLDING OF THE TRIANGULAR LATTICE IN THE FACE-CENTERED-CUBIC LATTICE WITH QUENCHED RANDOM SPONTANEOUS CURVATURE

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional face centered cubic lattice , in the presence of quenched random spontaneous curvature. We conside r two types of quenched randomness: (1) a 'physical' randomness arisin g from a prior random folding of the lattice, creating a preferred spo ntaneous curvature on the bonds; (2) a simple randomness where the spo ntaneous curvature is chosen at random independently on each bond. We study the folding transitions of the two models within the hexagon app roximation of the cluster variation method. Depending on the type of r andomness, the system shows different behaviours. We finally discuss a Hopfield-like model as an extension of the physical randomness proble m to account for the case where several different configurations are s tored in the prior prefolding process.