Renormalization-group theory of the Heisenberg model in d dimensions

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.(c) 2022 Elsevier B.V. All rights reserved.