We address the problem of "phantom" folding of the tethered membrane modeled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K1 and K2 for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding to a first-order (ferromagnetic) folding transition, and the other to a continuous (anti-ferromagnetic) unfolding transition.
- Phase transition
- Polymerized membrane
- Vertex model
ASJC Scopus subject areas
- Nuclear and High Energy Physics