Effective indirect multi-site spin-spin interactions in the s-d(f) model

TL;DR

This paper demonstrates that the dynamics of localized spins in the s-d(f) model can be effectively described by a spin model with multi-site interactions, derived using Matsubara Green's functions.

Contribution

It provides an exact representation of the effective spin model's action as an infinite series in the exchange interaction J, highlighting multi-site interactions.

Findings

Derived an exact series representation of the effective spin model

Identified multi-site spin-spin interactions of second, third, and fourth order

Provided insights into the indirect interactions in the s-d(f) model

Abstract

Using the diagram technique for Matsubara Green's functions it is shown that the dynamics of the localized spin subsystem in the s-d(f) model can be described in terms of an effective spin model with multi-site spin-spin interactions. An exact representation of the action for the effective purely spin model is derived as an infinite series in powers of s-d(f) exchange interaction $J$. The indirect interactions of the 2-nd, 3-rd and 4-th order are discussed.