  In this note we combine the "spin-argument" from [KLR15] and the
$n$-dimensional incompatible, one-well rigidity result from [LL16], in order to
infer a new proof for the compactness of discrete multi-well energies
associated with the modelling of surface energies in certain phase transitions.
Mathematically, a main novelty here is the reduction of the problem to an
incompatible one-well problem. The presented argument is very robust and
applies to a number of different physically interesting models, including for
instance phase transformations in shape-memory materials but also
anti-ferromagnetic transformations or related transitions with an "internal"
microstructure on smaller scales.
