Analysis of the migdal transformation for models with Heisenberg spins on a d-dimensional lattice

Abstract

We show for classical Heisenberg spins, with a general nearest neighbour interaction, that in the Migdal approximation the only low-temperature phase transitions are Ising ones (ferror antiferromagnetic). For d=2 neither the pure Heisenberg model nor the Lebwohl-Lasher model show a phase transition at a finite temperature. For d>2 transitions do exist at intermediate temperature and the complete flow diagram together with a two-parameter phase diagram is obtained numerically for d=3. Apart from critical temperatures and thermal exponents, also the magnetic exponents (for both Heisenberg and XY spins) are calculated. The latter are in very good agreement with exact results.