Nonequilibrium ferromagnetic spin-1 Blume–Capel model

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Abstract
We investigate the nonequilibrium phase diagram of the two-dimensional ferromagnetic spin-1 Blume-Capel model driven by competing stochastic dynamics. The system is simultaneously coupled to a thermal reservoir, modeled by single-spin-flip Glauber dynamics via the Metropolis algorithm, and subjected to a continuous external energy flux, simulated by two-spin-exchange Kawasaki dynamics. Using extensive Monte Carlo simulations, we characterize the stationary states, phase transitions, and the rich phase-diagram topology induced by this dynamical competition. Despite the ferromagnetic nature of the exchange interactions, the interplay between thermal relaxation and energy injection induces nonequilibrium self-organization, leading to the emergence of partially and fully ordered antiferromagnetic phases. Furthermore, we demonstrate that systematically varying the single-ion anisotropy shifts the position of the tricritical point and alters the extent of metastable regions exhibiting thermal hysteresis. Remarkably, finite-size scaling analyses reveal that even in the presence of steady energy fluxes and detailed-balance violation, the critical exponents of the continuous transitions remain consistent with the equilibrium two-dimensional Ising universality class to within numerical accuracy.

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