A Mechanism of Long-Range Order Induced by Random Local Fields: Effective Anisotropy Created by Defects

Abstract

We propose a microscopic mechanism of the long-range order in two-dimensional space induced by random local fields of crystal defects. The anisotropic distribution of defect-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry is shown to give rise to the defect-induced effective anisotropy in the system. The expression for the effective anisotropy constant is found. A weak anisotropy of the "easy axis" type transforms the X-Y model and the Heisenberg model to the class of Ising models, and brings into existence the long-range order in the system.

9 pages. arXiv admin note: substantial text overlap with arXiv:1603.03360

References in corpus (2)

• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases
• The anisotropy induced by defects of "random local field" type in O(n) models and suppression of the Imry-Ma inhomogeneous state

Cited by in corpus (4)

• Long-range order induced by random fields in two-dimensional O(n) models, and the Imry-Ma state
• Imry-Ma disordered state induced by defects of "random local anisotropy" type in the system with O(n) symmetry
• Cubic anisotropy created by defects of "random local anisotropy" type, and phase diagram of the O(n) model
• Phase diagram for the O(n) model with defects of "random local field" type and verity of the Imry-Ma theorem