Materials Science and Nanotechnology

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

International Conference on Magnetism and Magnetic Materials
October 09-10, 2017 London, UK

A S Sigov

Moscow Technological University, Russian Federation

Posters & Accepted Abstracts : Materials Science and Nanotechnology

Abstract:

After the publication in 1975 the classical paper by Imry and Ma, the viewpoint was firmly established in the literature that at 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, which in what follows will be designated as the Imry-Ma state and the statement given above will be named the Imry-Ma theorem. An anisotropic distribution of the directions of defect-induced random local fields in the order parameter n-dimensional space gives rise to the effective anisotropy in the system. Evaluation of the effective anisotropy constant Keff for strong anisotropic distributions in the order of magnitude gives the value Keff ~ x(hl)^2 / JS^2, where x is the defect concentration, hl is the local field induced by lth defect, J is the exchange interaction constant between neighboring spins and the brackets denote averaging over defects. The Imry-Ma theorem breaks down due to existence of the “easy axis” anisotropy induced by the defects designed initially for breaking down the long-range order. In the case of slightly anisotropic distribution of the fields, there exists a critical concentration of defects, if exceeded the ImryMa inhomogeneous state can exist as an equilibrium one. In the case of strongly anisotropic distribution of the fields, the Imry-Ma inhomogeneous state is completely suppressed and the state with the long-range ordering is realized at any defect concentration.

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