A mechanism of long-range order induced by random fields: Effective anisotropy created by defects

A microscopic mechanism of the long-range order in two-dimensional space induced by random local fields of crystal defects has been found. The impurity-induced effective anisotropy has been shown to arise in the system due to anisotropic distribution of impurity-induced random local field directions in the $n$-dimensional space of vector order parameter with the $O(n)$ symmetry. The expression for the effective anisotropy constant has been obtained. A weak anisotropy of the “easy axis” type transforms the $X$–$Y$ model and the Heisenberg model to the class of Ising models, and brings into long-range order existence in the system.