Long-range order induced by random fields in two-dimensional O(n) models, and the Imry-Ma state

TL;DR

This paper investigates how random local fields with anisotropic distributions affect two-dimensional O(n) models, revealing conditions under which long-range order can emerge despite the presence of disorder.

Contribution

It demonstrates that anisotropic random fields can induce long-range order in 2D O(n) models, altering phase transitions and the nature of order.

Findings

Weak anisotropy leads to a transition from paramagnetic to Imry-Ma phase.

Strong anisotropy causes a phase transition to an ordered state at finite temperature.

Weak anisotropy eliminates the BKT phase, enabling long-range order.

Abstract

The influence of defects of the "random local field" type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of random fields, with decreasing temperature there takes place a smooth transition from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imry-Ma phase with static fluctuations caused by fluctuations of the random field of defects. In the case of strong anisotropy of random fields, defects lead to an effective decrease in the number of components of the order parameter and the appearance of a phase transition to an ordered state at finite temperature. It is shown that in the case of the defect-free two-dimensional X-Y model, the appearance of an arbitrarily weak anisotropy in the two-dimensional space of the order parameter completely eliminates the appearance of the Berezinsky-Kosterlitz-Thouless phase and gives rise to the phase with the long-range order.