Phase diagram for the O(n) model with defects of "random local field" type and verity of the Imry-Ma theorem

TL;DR

This paper investigates how anisotropic distributions of random local fields affect the validity of the Imry-Ma theorem in the O(n) model, revealing conditions under which long-range order persists or is destroyed.

Contribution

It demonstrates that the Imry-Ma theorem does not hold universally and identifies the role of defect-induced anisotropy in maintaining long-range order in the O(n) model.

Findings

Anisotropic defect distributions can prevent the Imry-Ma state in certain conditions.

Existence of a critical defect concentration for inhomogeneous Imry-Ma states in 2<d<4.

Strong anisotropy suppresses the Imry-Ma state entirely.

Abstract

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 field" 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 the occurrence of a disordered state, is not true if the anisotropic distribution of the defect-induced random local field directions in the n-dimensional space of the order parameter leads to the defect-induced effective anisotropy of the "easy axis" type. For a weakly anisotropic field distribution, in space dimensions 2<d<4 there exists some critical defect concentration, above which 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 field distribution, the Imry-Ma state is suppressed completely and the long-range order state takes place at any defect concentration.