Spin-lattice coupling as environmental effect

The exchange constant in a magnetic system results from the overlap of orbitals, so it depends upon the ion distance and yields a coupling with the lattice vibrations: this can strongly influence the statistical mechanics of magnets. As the fast lattice dynamics allows for a rapid thermalization, phonon-induced spin correlations can be reasonably neglected, so that phonons can be regarded as a thermalized environment (or bath) for the spins. It is therefore natural to treat it within a Caldeira-Leggett scheme, i.e., by the influence action obtained after tracing-out the bath's degrees of freedom, whose contribution can be accounted for within a known semiclassical approach. In this way extended phase diagrams, accounting for the environmental interaction, can be drawn for the magnetic phase transitions.