Far-from-equilibrium growth of magnetic thin films with Blume-Capel impurities

We investigate the irreversible growth of (2+1)-dimensional magnetic thin films. The spin variable can adopt three states (s(I)=±1,0), and the system is in contact with a thermal bath of temperature T. The deposition process depends on the change of the configuration energy, which, by analogy to the Blume-Capel Hamiltonian in equilibrium systems, depends on Ising-like couplings between neighboring spins (J) and has a crystal field (D) term that controls the density of nonmagnetic impurities (s(I)=0). Once deposited, particles are not allowed to flip, diffuse, or detach. By means of extensive Monte Carlo simulations, we obtain the phase diagram in the crystal field vs temperature parameter space. We show clear evidence of the existence of a tricritical point located at D(t)/J=1.145(10) and k(B)T(t)/J=0.425(10), which separates a first-order transition curve at lower temperatures from a critical second-order transition curve at higher temperatures, in analogy with the previously studied equilibrium Blume-Capel model. Furthermore, we show that, along the second-order transition curve, the critical behavior of the irreversible growth model can be described by means of the critical exponents of the two-dimensional Ising model under equilibrium conditions. Therefore, our findings provide a link between well-known theoretical equilibrium models and nonequilibrium growth processes that are of great interest for many experimental applications, as well as a paradigmatic topic of study in current statistical physics.