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Mater Sci Nanotechnol 2017
Volume 1 Issue 3
Magnetic Materials 2017
Page 97
October 09-10, 2017 London, UK
International Conference on
Phase diagram for the O(n) model with defects
of “random local field” type and verity of the
Imry-Ma theorem
A S Sigov
Moscow Technological University, Russian Federation
A
fter 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 K
eff
for strong anisotropic distributions
in the order of magnitude gives the value K
eff
~
x(hl
)^2 /
JS^2, where
x
is the defect concentration, h
l
is the local field
induced by
l
th
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 Imry-
Ma 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.
assigov@yandex.ruMaterials Science and Nanotechnology