A Mechanism of Long-Range Order Induced by Random Local Fields:   Effective Anisotropy Created by Defects
  We propose a microscopic mechanism of the long-range order in two-dimensional space induced by random local fields of crystal defects. The anisotropic distribution of defect-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry is shown to give rise to the defect-induced effective anisotropy in the system. The expression for the effective anisotropy constant is found. 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 existence the long-range order in the system. 
A.A. Berzin, A.I. Morosov, and A.S. Sigov
cond-mat.dis-nn cond-mat.stat-mech