Mean field analysis of two coupled Heisenberg models

We have derived and analyzed the Landau free energy for two coupled Heisenberg subsystems in the general case of n-component order parameters. The calculation was done in the weak-coupling limit when the exchange interactions J1 and J2 in the subsystems exceed the intersubsystem interaction K. There exist two stable collinear phases, depending on the sign of K. The phase transitions to the stable phases are of second order for the whole range of parameters of the model under consideration. The numerical calculations show that for positive sign of interactions two more phases exist, which are metastable or unstable depending on the number of the order parameter components n