Journal of Physical Studies 5(1), 49–64 (2001) DOI: https://doi.org/10.30970/jps.05.49 JORDAN–WIGNER FERMIONIZATION FOR SPIN-½ SYSTEMS IN TWO DIMENSIONS: A BRIEF REVIEW O. Derzhko Institute for Condensed Matter Physics% of the National Academy of Sciences of Ukraine 1 Svientsitskii Street, Lviv-11, UA-79011, Ukraine and Ivan Franko National University of Lviv, Chair of Theoretical Physics 12 Drahomanov Str., Lviv-5, UA-79005, Ukraine

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-$\frac{1}{2}$ models. We discuss in some detail the two-dimensional spin-$\frac{1}{2}$ isotropic $XY$ and Heisenberg models.

PACS number(s): 75.10.-b

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