  In this article we study scaling laws for simplified multi-well nucleation
problems without gauge invariances which are motivated by models for
shape-memory alloys. Seeking to explore the role of the order of lamination on
the energy scaling for nucleation processes, we provide scaling laws for
various model problems in two and three dimensions. In particular, we discuss
(optimal) scaling results in the volume and the singular perturbation parameter
for settings in which the surrounding parent phase is in the first, the second
and the third order lamination convex hull of the wells of the nucleating
phase. Furthermore, we provide a corresponding result for the setting of an
infinite order laminate which arises in the context of the Tartar square. In
particular, our results provide isoperimetric estimates in situations in which
strong nonlocal anisotropies are present.
