Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

TL;DR

This paper investigates spin-S bilayer Heisenberg models using mean-field and numerical methods, revealing a continuous phase transition between dimer and Neel phases for various S, and showing S=1 layers behave like S=1/2 layers.

Contribution

It provides a comprehensive analysis of phase transitions in spin-S bilayer Heisenberg models, challenging previous theories and demonstrating the similarity between S=1 and S=1/2 layers.

Findings

Transition between dimer and Neel phases is continuous for all S.

S=1 layers behave similarly to S=1/2 layers.

Supports a unified picture of the order-disorder phase transition.

Abstract

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.