Sequence of phase transitions induced in an array of Josephson junctions by their crossover to π-state

We show that the transition of Josephson junctions between the conventional and π states caused by the decrease in temperature induces in a regular two-dimensional array of such junctions not just a single phase transition between two phases with different ordering but a sequence of two, three or four phase transitions. The corresponding phase diagrams are constructed for the cases of bipartite (square or honeycomb) and triangular lattices.