  We discuss a disordered $\lambda\varphi^{4}+\rho\varphi^{6}$ Landau-Ginzburg
model defined in a d-dimensional space. First we adopt the standard procedure
of averaging the disorder dependent free energy of the model. The dominant
contribution to this quantity is represented by a series of the replica
partition functions of the system. Next, using the replica symmetry ansatz in
the saddle-point equations, we prove that the average free energy represents a
system with multiple ground states with different order parameters. For low
temperatures we show the presence of metastable equilibrium states for some
replica fields for a range of values of the physical parameters. Finally, going
beyond the mean-field approximation, the one-loop renormalization of this model
is performed, in the leading order replica partition function.
