Determine which mean-field decoupling best describes physical underscreened Kondo lattices

Determine whether performing the first-order 1/N expansion and extrapolating to N=2, or setting N=2 from the outset, more accurately describes physical spin-1 underscreened Kondo lattice systems.

Background

The paper develops a variational framework that connects two previously used mean-field treatments of the spin-1 underscreened Kondo lattice. In the first treatment, one performs a controlled expansion around the N→∞ saddle point and then extrapolates the result to the physical value N=2. In the second, one sets N=2 at the outset and applies the variational decoupling directly.

These approaches produce different structures for the phase in which Kondo hybridization coexists with magnetic order: the extrapolated large-N treatment yields a strong-Kondo ferromagnetic regime, whereas the direct N=2 treatment yields a weak-Kondo ferromagnetic regime. The paper argues conditionally that the first approach may be more reliable when Kondo hybridization dominates and the second may be preferable when magnetic and Kondo interactions are comparably important, but it does not establish which treatment is generally closer to real physical systems.