Folding transitions of the square – diagonal two – dimensional lattice ∗

The phase diagram of a vertex model introduced by P. Di Francesco (Nucl. Phys. B 525, 507 1998) representing the configurations of a square lattice which can fold with different bending energies along the main axes and the diagonals has been studied by Cluster Variation Method. A very rich structure with partially and completely folded phases, different disordered phases and a flat phase is found. The crumpling transition between a disordered and the flat phase is first–order. The CVM results are confimed by the analysis of the ground states and of the two limits where the model reduces to an Ising model. PACS numbers: 05.50.+q (Ising problems); 64.60.-i (General studies of phase transitions); 82.65.Dp (Thermodynamics of surfaces and interfaces).