  We studied the critical behavior of the $J_{1}-J_{2}$ spin-{1/2} Ising model
in the square lattice by considering $J_{1}$ fixed and $J_{2}$ as random
interactions following discrete and continuous probability distribution
functions. The configuration of $J_{2}$ in the lattice evolves in time through
a competing kinetics using Monte Carlo simulations leading to a steady state
without reaching the free-energy minimization. However, the resulting
non-equilibrium phase diagrams are, in general, qualitatively similar to those
obtained with quenched randomness at equilibrium in past works. Accordingly,
through this dynamics the essential critical behavior at finite temperatures
can be grasped for this model. The advantage is that simulations spend less
computational resources, since the system does not need to be replicated or
equilibrated with Parallel Tempering. A special attention was given for the
value of the amplitude of the correlation length at the critical point of the
superantiferromagnetic-paramagnetic transition.
