The possibility of hysteretic behaviours in plane monolayers of electr
ic dipoles is investigated. The basic tool for this study is a model w
here the electric dipoles can rotate around the nodes of a plane rhomb
ic grid and the electric interactions among dipoles are properly simpl
ified (Union Jack approximation). In the ideal case of an infinitely e
xtending monolayer, the model yields analytical solutions both for the
spatially periodical equilibrium orientations of dipoles and for thei
r stability under the influence of an external electric field. On this
basis, a set of hysteresis cycles dealing with different physical sit
uations is obtained and discussed. Then, the much more realistic and c
omplex case of finite-size dipole- monolayers is considered and the hy
steresis cycles are obtained by computer calculations. The degree of s
imilarity of these numerical results with the analytical ones of the c
orresponding infinitely extending monolayers puts into evidence the pr
ediction capabilities of such simple model.