Gauge equivalence between one-dimensional Heisenberg ferromagnets with single-site anisotropy and nonlinear Schrodinger equations

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Abstract
The concept of gauge equivalence is introduced for the classical one-dimensional Heisenberg ferromagnets with single-site anisotropy. The classical continuum version of the one-dimensional anisotropic Heisenberg antiferromagnet (ferromagnet) of spin 1/2 is shown to be gauge-equivalent to the nonlinear Schrodinger equation with the repulsive (attractive) interaction, which is consistent with the Yang and Yang statement on thermodynamical equivalence between the corresponding quantum systems.