Non-affine fluctuations and the Statistics of Defect Precursors in the Planar Honeycomb Lattice

TL;DR

This paper investigates non-affine displacement fluctuations in the planar honeycomb lattice, identifying their role as precursors to topological defects and analyzing their statistical behavior at finite temperatures.

Contribution

It provides an exact statistical analysis of precursor modes in a harmonic honeycomb lattice, linking non-affine fluctuations to defect formation.

Findings

Precursor fluctuations are among the most pronounced non-affine distortions.

As interactions destabilize the solid, fluctuations diverge and correlations become long-ranged.

Exact single point and two-point distributions of precursor modes are obtained.

Abstract

Certain localised displacement fluctuations in the planar honeycomb lattice may be identified as precursors to topological defects. We show that these fluctuations are among the most pronounced {\em non-affine} distortions of an elemental coarse graining volume of the honeycomb structure at non zero temperatures. We obtain the statistics of these precursor modes in the canonical ensemble, evaluating exactly their single point and two-point spatio-temporal distributions, for a lattice with harmonic nearest neighbour and next near neighbour bonds. As the solid is destabilised by tuning interactions, the precursor fluctuations diverge and correlations become long-lived and long-ranged.