Two-dimensional O(n) Models with Defects of "Random Local Anisotropy" Type

TL;DR

This paper investigates the phase diagram of two-dimensional O(n) models with defects of random local anisotropy, revealing transitions from paramagnetic to Imri-Ma phases and to ordered states depending on anisotropy strength.

Contribution

It provides a detailed analysis of phase transitions in 2D O(n) models with random local anisotropy, highlighting the conditions for different universality classes.

Findings

Transition from paramagnetic to Imri-Ma phase with decreasing temperature.

Existence of a finite-temperature phase transition to an ordered state under strong anisotropy.

Identification of universality class shifts based on anisotropy strength.

Abstract

The phase diagram of two-dimensional systems with continuous symmetry of the vector order parameter containing defects of the "random local anisotropy" type is investigated. In the case of a weakly anisotropic distribution of the easy anisotropy axes in the space of the order parameter, with decreasing temperature, a smooth transition takes place from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imri-Ma phase with its static fluctuations. In the case when the anisotropic distribution of the easy axes induces a global anisotropy of the "easy axis" type that exceeds a critical value, the system goes into the Ising class of universality, and a phase transition to the ordered state occurs in it at a finite temperature.