Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory

TL;DR

This paper applies Fourier-Legendre renormalization-group theory to solve the random-field Heisenberg model in dimensions greater than two, revealing reentrant ferromagnetic order at three dimensions as temperature varies.

Contribution

It introduces a novel Fourier-Legendre RG approach to exactly solve the random-field Heisenberg model across multiple hierarchical dimensions.

Findings

Ferromagnetic order exists for d>2 with non-zero random fields.

Reentrant ferromagnetic behavior observed at d=3 as temperature changes.

Exact solutions obtained for multiple hierarchical models.

Abstract

The random-magnetic-field classical Heisenberg model is solved in spatial dimensions d>=2 using the recently developed Fourier-Legendre renormalization-group theory for $4\pi$ steradians continuously orientable spins, with renormalization-group flows of 12,500 variables. The random-magnetic-field Heisenberg model is exactly solved in 10 hierarchical models, for d=2,2.26,2.46,2.58,2.63,2.77,2.89,3. For non-zero random fields, ferromagnetic order is seen for d>2. This ordering shows, at d=3, reentrance as a function of temperature.