Folding transitions in three-dimensional space with defects

TL;DR

This paper models three-dimensional folding of a triangular lattice with defects, revealing how defects convert first-order crumpling transitions into continuous ones and lead to new phases.

Contribution

It generalizes a folding model to include defects, analyzes phase transitions, and identifies how defect energy influences transition types and phase structure.

Findings

Defects turn first-order transitions into continuous ones

Lower defect energy introduces new phases

Defect densities exhibit specific behaviors

Abstract

A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed in terms of Ising-like variables with nearest-neighbor and plaquette interactions in the hexagonal lattice; its phase diagram is determined by the Cluster Variation Method. The results found by varying the curvature and defect energy show that the introduction of defects turns the first-order crumpling transitions of the model without defects into continuous transitions. New phases also appear by decreasing the energy cost of defects and the behavior of their densities has been analyzed.