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

• Lattice magnon Hamiltonian constructed from the effective Lagrangian.
• New Feynman diagrams with colored propagators and vertices for lattice scalar fields.
• Influence of magnon–magnon interactions from the WZW term on magnon energies and free energy of O(3) HFM.

We present the perturbation theory for lattice magnon fields of the DD-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).