  We study the competition between ferromagnetic and spin glass phases using a
system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We
obtain the replica-symmetric solution for the free energy of this system in
terms of magnetization and Edwards-Anderson order parameters in both
subsystems. Using these order parameters we are able to identify different
phases in the system and determine which phase is dominant for different
strengths of the coupling between two subsystems. We observe that both
subsystems are in the same phase although with different order parameters. The
phase boundary between paramagnetic-ferromagnetic and paramagnetic-spin glass
phases is more or less similar to that in the Sherrington-Kirkpatrick phase
diagram. But the boundary between ferromagnetic-spin glass phases becomes
qualitatively different as the coupling between the two subsystems changes.
Remarkably, for intermediate values of the coupling, this phase boundary is
such that there could be a reentrant transition between spin glass and
ferromagnetic phases by increasing the temperature. We found that for some
range of the coupling, the second order transition between these phases turns
into first order at a tricritical point. Further, we carry out the stability
analysis by considering deviations from the replica symmetric solution.
