The dressing effect due to the quantum nature of phonons may cause the creation of bound states of several vibrons in the molecular chain. The possibility of creating soliton states of this type is discussed for the simple Fröhlich one-dimensional model. The regions of the system parameter space where different mechanisms dominate the behaviour of such entities are characterized.

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).

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