  We study the discrete-to-continuum limit of ferromagnetic spin systems when
the lattice spacing tends to zero. We assume that the atoms are part of a
(maybe) non-periodic lattice close to a flat set in a lower dimensional space,
typically a plate in three dimensions. Scaling the particle positions by a
small parameter $\varepsilon>0$ we perform a $\Gamma$-convergence analysis of
properly rescaled interfacial-type energies. We show that, up to subsequences,
the energies converge to a surface integral defined on partitions of the flat
space. In the second part of the paper we address the issue of stochastic
homogenization in the case of random stationary lattices. A finer dependence of
the homogenized energy on the average thickness of the random lattice is
analyzed for an example of magnetic thin system obtained by a random deposition
mechanism.
