Octupolar order in two dimensions

TL;DR

This paper explores octupolar order in two-dimensional systems using a tensor-based approach, revealing an equivalence between probability density maxima and tensor diagonalization specific to two dimensions.

Contribution

It introduces a tensor-based framework for describing octupolar order in 2D and establishes an equivalence between probability maxima and tensor diagonalization.

Findings

Octupolar order characterized by third-rank symmetric traceless tensors.

Maxima and minima of probability density relate to tensor properties.

Equivalence between density maxima and tensor diagonalization is unique to 2D.

Abstract

Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be equivalent to diagonalizing the relevant third-rank tensor, an equivalence which however is only valid in the two-dimensional case.