Nonequilibrium study of the $J_{1}-J_{2}$ Ising model with random $J_{2}$ couplings in the square lattice

Abstract: 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.