Is there a spin-glass phase in the random temperature Ising ferromagnet?

In this paper we study the phase diagram of the disordered Ising ferromagnet. Within the framework of the Gaussian variational approximation it is shown that in systems with a finite value of the disorder in dimensions D = 4 and D < 4 the paramagnetic and ferromagnetic phases are separated by a spin-glass phase. The transition from paramagnetic to spin-glass state is continuous (second order), whereas the transition between spin-glass and ferromagnetic states is discontinuous (first order). It is also shown that within the considered approximation there is no replica symmetry breaking in the spin-glass phase. The validity of the Gaussian variational approximation for the present problem is discussed, and we provide a tentative physical interpretation of the results.