Folding transition of the triangular lattice in a discrete three-dimensional space.

A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter [Nucl. Phys. B 450, 463 (1995)] describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three–dimensional space. We have introduced a curvature energy and a symmetry breaking field and studied the phase diagram of the resulting model. By varying the curvature energy parameter, a first-order transition has been found between a flat and a folded phase for any value of the symmetry breaking field. PACS numbers: 05.50.+q (Ising problems); 64.60.-i (General studies of phase transitions); 82.65.Dp (Thermodynamics of surfaces and interfaces). (∗) Permanent Address: Dipartimento di Fisica dell’Università di Bari and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Amendola 173, 70126 Bari, Italy