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 (1998) 507) 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 confirmed by the analysis of the ground states and of the two limits where the model reduces to an Ising model