  Dipolar Bose-Einstein condensates in an array of double-well potentials
realize an effective transverse Ising model with peculiar inter-layer
interactions, that may result under proper conditions in an anomalous
first-order ferromagnetic-antiferromagnetic phase transition, and nontrivial
phases due to frustration. The considered setup as well allows the study of
Kibble-Zurek defect formation, whose kink statistics follows that expected from
the universality class of the mean-field transverse Ising model in 1D.
Furthermore, random occupation of each layer of the stack leads to random
effective Ising interactions and generation of local transverse fields, thus
allowing the study of Anderson-like localization of imbalance perturbations in
the two-well stack under controllable conditions.
