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

TL;DR

This paper introduces a microscopic mechanism where defects induce effective anisotropy in two-dimensional systems, leading to long-range order by transforming models like XY and Heisenberg into Ising-like systems.

Contribution

It demonstrates how anisotropic distributions of defect-induced local fields create effective anisotropy, enabling long-range order in 2D systems with O(n) symmetry.

Findings

Effective anisotropy constant derived

Weak anisotropy induces long-range order

Transformation of XY and Heisenberg models to Ising models

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.