Folding Transitions of the Square-Diagonal Lattice

TL;DR

This paper investigates the folding behavior of a square-diagonal lattice model with bending rigidities, deriving its complete phase diagram and identifying two distinct folding transitions through transfer matrix calculations.

Contribution

The study provides the first comprehensive phase diagram for the square-diagonal lattice folding model with two bending rigidities, revealing both first-order and continuous transitions.

Findings

Identified a first-order ferromagnetic folding transition.

Discovered a continuous anti-ferromagnetic unfolding transition.

Mapped the complete phase diagram of the model.

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.