Basic model of ferromagnetic solids:
atoms are fixed on the vertices of a lattice. Their
dipole vectors (spins) may have varying directions: either
up/down (Ising model) or any direction (Heisenberg model).

Microscopic configuration
: given by
the spins on the lattice.

Example:
Two-dimensional square Ising lattice; only the four nearest spins
contribute to the energy of spin
(). (Three dimensions: six nearest neighbors).
The total energy is

( ... coupling constant).

Magnetic polarization

may be determined as a function of temperature.
If a magnetic field is applied,
the additional potential energy is
.
F. J. Vesely / University of Vienna