Tunca, EgemenBerker, A. Nihat2023-10-192023-10-19202220378-43711873-2119https://doi.org/10.1016/j.physa.2022.128300https://hdl.handle.net/20.500.12469/5158The 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.(c) 2022 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/openAccessHierarchical LatticesPhase-TransitionsMigdal-KadanoffPotts ModelsSpin SystemsFieldHierarchical LatticesPhase transitionsPhase-TransitionsSpin modelsMigdal-KadanoffFree energyPotts ModelsInternal energySpin SystemsSpecific heatFieldRenormalization-group theoryArticle608WOS:00091202980000110.1016/j.physa.2022.1283002-s2.0-85142763874Q2Q2