  We develop a fully microscopic, statistical mechanics approach to study phase
transitions in Ising systems with competing interactions at different scales.
Our aim is to consider orientational and positional order parameters in a
unified framework. In this work we consider two dimensional stripe forming
systems, where nematic, smectic and crystal phases are possible. We introduce a
nematic order parameter in a lattice, which measures orientational order of
interfaces. We develop a mean field approach which leads to a free energy which
is a function of both the magnetization (density) and the orientational
(nematic) order parameters. Self-consistent equations for the order parameters
are obtained and the solutions are described for a particular system, the
Dipolar Frustrated Ising Ferromagnet. We show that this system has an
Ising-nematic phase at low temperatures in the square lattice, where positional
order (staggered magnetization) is zero. At lower temperatures a crystal-stripe
phase may appear. In the continuum limit the present approach connects to a
Ginsburg-Landau theory, which has an isotropic-nematic phase transition with
breaking of a continuous symmetry.
