Phase transitions in 2-dimensional systems of migrating orientable lattice defects

Phase transitions are studied in a system consisting of reorientating and migrating point defects in a two dimensional lattice. Due to the long range (r ^–2) nature of the dominant elastic interaction, surface effects are of central importance and have to be included. After diagonalizing the elastic interaction energy for defects characterized by arbitrary elastic dipole tensors the free energy of the system is minimized with respect to the tensor defect density (which describes the defect distribution in space and over a discrete number of orientations). Different types of phase transitions are obtained depending on the magnitude of the defect anisotropy. The phase below the paraelastic one is characterized for large by an anisotropic but homogeneous distribution, for small by an anisotropic and inhomogeneous distribution with a non linear space dependence. Similarities and differences with 3d results for=0 (or small) are discussed.