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Jordan–Wigner fermionization for spin-½ systems in two dimensions: A brief review

Jordan–Wigner fermionization for spin-½ systems in two dimensions: A brief review

We review the papers on the Jordan-Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two-dimensional spin-1/2 models. We discuss in some detail the two-dimensional spin-1/2 isotropic XY and Heisenberg models.