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arXiv · 2202.06049

Renormalization-Group Theory of the Heisenberg Model in d Dimensions

Egemen Tunca·A. Nihat Berker
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Abstract

The classical Heisenberg model has been solved in spatial d dimensins, exactly in d=1 and by the Migdal-Kadanoff approximation in d>1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the specific heats are calculated in arbitrary dimension d. Fisher's exact result is recovered in d=1. The absence of an ordered phase, conventional or algebraic (in contrast to the XY model yielding an algebraically ordered phase), is recovered in d=2. A conventionally ordered phase occurs at d>2. This method opens the way to complex-system calculations with Heisenberg local degrees of freedom.

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Egemen Tunca, A. Nihat Berker. 2022-02-12. Renormalization-Group Theory of the Heisenberg Model in d Dimensions. https://doi.org/10.1016/j.physa.2022.128300

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