| A magnetic system is usually described in terms of the exchange coupling between neighboring spins lying on the sites of a given lattice. The interaction can display anisotropy, and the Hamiltonian can also contain additional terms describing, e.g., the effect of a uniform magnetic field. With these ingredients a vaste zoology of thermodynamic behaviors can occur, and phase transitions of different universality classes can arise in more than one dimension. We are interested here in introducing in this framework the unavoidable quantum environmental effects due to the coupling with the underlying lattice. While magnon-phonon hybridization phenomena were extensively studied in the past, additional effects can arise from the modifications of the density matrix due to heat transfer between spin excitations and phonon degrees of freedom. By applying a Caldeira-Leggett scheme it is possible to evaluate such effects through the analysis of the associated influence action, obtained after tracing-out the environmental degrees of freedom. The corresponding path integral can be evaluated within the pure-quantum self-consistent harmonic approximation. In this way one can obtain extended phase diagrams for the magnetic phase transitions, accounting for the environmental interaction. |
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