  In the paper a self-consistent theoretical description of the lattice and
magnetic properties of a model system with magnetoelastic interaction is
presented. The dependence of magnetic exchange integrals on the distance
between interacting spins is assumed, which couples the magnetic and the
lattice subsystem. The framework is based on summation of the Gibbs free
energies for the lattice subsystem and magnetic subsystem. On the basis of
minimization principle for the Gibbs energy, a set of equations of state for
the system is derived. These equations of state combine the parameters
describing the elastic properties (relative volume deformation) and the
magnetic properties (magnetization changes).
  The formalism is extensively illustrated with the numerical calculations
performed for a system of ferromagnetically coupled spins $S$=1/2 localized at
the sites of simple cubic lattice. In particular, the significant influence of
the magnetic subsystem on the elastic properties is demonstrated. It manifests
itself in significant modification of such quantities as the relative volume
deformation, thermal expansion coefficient or isothermal compressibility, in
particular, in the vicinity of the magnetic phase transition. On the other
hand, the influence of lattice subsystem on the magnetic one is also evident.
It takes, for example, the form of dependence of the critical (Curie)
temperature and magnetization itself on the external pressure, which is
thoroughly investigated.
