Symmetries of the Classical Heisenberg Model

Abstract

The symmetries of the classical Heisenberg model are investigated. It is shown that such symmetries are groups of conformal transformations and rotations. The invariance of vortex structures with respect to the rotation group is studied. Application of the found transformations of the field rotation group to the previously found solutions of the Heisenberg model (such as instantons, vortex “targets” and “spirals”) generates other structures, which are also solutions to this model, the properties of which are determined by the original structures. which are also solutions of this model, with the properties determined by the original structures.