Magnon Energy Renormalization and Low-Temperature Thermodynamics of O(3) Heisenberg Ferromagnets

TL;DR

This paper develops a perturbation theory for lattice magnons in D-dimensional O(3) Heisenberg ferromagnets, analyzing magnon interactions and their effects on energy renormalization and thermodynamics at low temperatures.

Contribution

It introduces a detailed perturbation framework based on effective Lagrangian and Hamiltonian, highlighting the roles of gradient and Wess-Zumino-Witten terms in magnon interactions.

Findings

Magnon-magnon interactions significantly influence magnon self-energy.

The effective Hamiltonian captures dominant interaction effects.

Spurious terms in low-temperature free energy series are identified.

Abstract

We present the perturbation theory for lattice magnon fields of $D$-dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon-magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess-Zumino-Witten term of effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on basis of which we investigate the influence of magnon-magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in the low-temperature series for the free energy by examining magnon-magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian).