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

TL;DR

This paper investigates the folding transition of a triangular lattice in a discrete 3D space using a vertex model, revealing a first-order phase transition between flat and folded states influenced by curvature energy.

Contribution

It introduces a curvature energy and symmetry breaking field into a vertex model and analyzes the phase diagram, identifying a first-order transition in the folding behavior.

Findings

First-order transition between flat and folded phases.

Phase diagram influenced by curvature energy and symmetry breaking.

Model describes polymerized membrane behavior in discrete 3D space.

Abstract

A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter (cond-mat/9502063) 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.