Eur. Phys. J. E (2015) 38: 63
https://doi.org/10.1140/epje/i2015-15063-x

Regular Article

Octupolar order in two dimensions

Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, I-27100, Pavia, Italy

^* e-mail: eg.virga@unipv.it

Received: 15 March 2015
Revised: 29 April 2015
Accepted: 11 May 2015
Published online: 29 June 2015

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.