Renormalization-group theory of the Heisenberg model in d dimensions

Egemen Tunca and A. Nihat Berker

Physica A: Statistical Mechanics and its Applications, 2022, vol. 608, issue P2

Abstract: The classical Heisenberg model has been solved in spatial d dimensions, 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.

Keywords: Phase transitions; Spin models; Free energy; Internal energy; Specific heat; Renormalization-group theory (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:608:y:2022:i:p2:s0378437122008585

DOI: 10.1016/j.physa.2022.128300

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