Cubic anisotropy created by defects of "random local anisotropy" type, and phase diagram of the O(n) model

TL;DR

This paper derives the cubic anisotropy constant caused by defects with random local anisotropy and explores how defect distribution affects the phase diagram of the O(n) model, challenging the traditional Imry-Ma theorem.

Contribution

It introduces a new expression for the defect-induced cubic anisotropy constant and analyzes how anisotropic defect distributions influence long-range order in the O(n) model.

Findings

Anisotropic defect distribution can create a global easy axis anisotropy.

Critical defect concentration exists for weak anisotropy distributions in 2<d<4.

Strong anisotropy distribution suppresses the Imry-Ma state at all defect concentrations.

Abstract

The expression for the cubic-type-anisotropy constant created by defects of "random local anisotropy" type is derived. It is shown that the Imry-Ma theorem stating that in space dimensions d<4 the introduction of an arbitrarily small concentration of defects of the "random local anisotropy" type in a system with continuous symmetry of the n-component vector order parameter (O(n) model) leads to the long-range order collapse and to occurrence of a disordered state, is not true if an anisotropic distribution of the defect-induced random easy axes directions in the order parameter space creates a global effective anisotropy of the "easy axis" type. For a weakly anisotropic distribution of the easy axes, in space dimensions 2<d<4 there exists some critical defect concentration, when exceeded, the inhomogeneous Imry-Ma state can exist as an equilibrium one. At lower defect concentration the long-range order takes place in the system. For a strongly anisotropic distribution of the easy axes, the Imry-Ma state is suppressed completely and the long-range order state takes place at any defect concentration.