Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets

Abstract

We present the perturbation theory for lattice magnon fields of the 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 the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the 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 low-temperature series for the free energy by examining magnon-magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian). © 2013 Elsevier Inc.