Folding Transition of the Triangular Lattice

TL;DR

This paper investigates the phase transitions of a folded triangular lattice influenced by bending rigidity and magnetic field, revealing three distinct phases and a triple point through numerical transfer matrix analysis.

Contribution

It introduces a detailed numerical analysis of the folding transitions of a triangular lattice under bending rigidity and magnetic field, identifying multiple phase boundaries and a triple point.

Findings

Three first order transition lines in the (K,h) plane

Existence of a folded phase and flat phases with all normals up or down

Identification of a triple point at K_c=0.11(1)

Abstract

We study the problem of folding of the regular triangular lattice in the presence of bending rigidity K and magnetic field h (conjugate to the local normal vectors to the triangles). A numerical study of the transfer matrix of the problem shows the existence of three first order transition lines in the (K,h) plane separating three phases: a folded phase, a phase frozen in the completely flat configuration (with all normal vectors pointing up) and its mirror image (all normal vectors pointing down). At zero magnetic field, a first order folding transition is found at a positive value K_c=0.11(1) of the bending rigidity, corresponding to a triple point in the phase diagram.