Folding Transitions of the Square-Diagonal Lattice

Abstract

We address the problem of "phantom" folding of the tethered membrane modelled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities $K_1$ and $K_2$ 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.

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References in corpus (1)

• Folding the Square-Diagonal Lattice

Cited by in corpus (4)

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• Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
• Folding transitions of the square--diagonal two--dimensional lattice