Renormalization-Group Theory of the Heisenberg Model in d Dimensions

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.

5 pages, 5 figures

References in corpus (4)

• The Blume-Capel Model on Hierarchical Lattices: exact local properties
• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• First-Order to Second-Order Phase Transition Changeover and Latent Heats of q-State Potts Models in d=2,3 from a Simple Migdal-Kadanoff Adaptation
• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line

Cited by in corpus (5)

• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
• Thermodynamical behavior of the Blume-Capel model in the vicinity of its tricritical point
• Nematic Ordering in the Heisenberg Spin-Glass System in d=3 Dimensions
• Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory
• XY-Ashkin-Teller Phase Diagram in d=3