A generalized spin-1 Blume-Capel model with distance/volume dependent nearest-neighbor exchange interaction is introduced and investigated using the standard methods of statistical mechanics. Besides of the volume-dependent magnetic energy, the static electromagnetic energy and anharmonic Einstein phonon contribution are also taken into account. Taking the simple volume dependence of all energy contributions we have obtained the equation of state, magnetic moment, internal and Helmholtz free energy of the system. The ground-state and nite-temperature phase diagrams are obtained and discussed in detail. Is it shown that the generalized spin-1 Blume-Capel model exhibits a novel critical behavior appearing due to magnetostriction and thermal volume variations. The presented approach is very universal and easily applicable to many other theoretical models in different elds of solid state physics.

A generalized spin-1/2 transverse field Ising model with a negative thermal expansion of the lattice is introduced and investigated using standard methods of statistical mechanics. Besides the volume-dependent magnetic energy, the static lattice energy, and anharmonic Einstein phonon energy are also considered in calculations. Analytic relations for the Gibbs free energy, magnetic moments, and equations of state are obtained, taking into account a simple volume dependence of all energy contributions. The ground-state and finite-temperature phase diagrams are discussed in detail for the strong and weak magneto-elastic coupling. It is clearly demonstrated that the generalized spin-1/2 transverse field Ising model exhibits a novel critical behavior, due to the strong negative expansion of the lattice, which is controlled by the strength of magneto-elastic coupling. The presented approach can be easily modified to study also other magnetic and non-magnetic crystalline models of solids.