  We derive thermodynamic functionals for spatially inhomogeneous magnetization
on a torus in the context of an Ising spin lattice model. We calculate the
corresponding free energy and pressure (by applying an appropriate external
field using a quadratic Kac potential) and show that they are related via a
modified Legendre transform. The local properties of the infinite volume Gibbs
measure, related to whether a macroscopic configuration is realized as a
homogeneous state or as a mixture of pure states, are also studied by
constructing the corresponding Young-Gibbs measures.
