Nonequilibrium Phase Transition in a 2D Ferromagnetic Spins with Effective Interactions

The study of nonequilibrium steady-state (NESS) in the Ising model offers rich insights into the properties of complex systems far from equilibrium. This paper explores the nature of NESS phase transitions in two-dimensional (2D) ferromagnetic Ising model on a square lattice under effective interactions using Monte Carlo (MC) algorithms. This requires extensive MC simulations using the modified Metropolis and modified Glauber update rules. The qualification of the modified update rules is characterized by the definition of an effective parameter $h$. For $|h|>1$, it is analytically shown that the nature of the phase transition (including the critical temperature) is independent of $h$. Furthermore, for $-1<h<1$, we study the steady-state properties of phase transitions using numerical methods. Therefore, we performed simulations for different lattice sizes and measured relevant physical quantities. From the data, we determined the numerical results of the transition temperature and relevant critical exponents for various values of $h$ by applying finite-size scaling (FSS). We found that the FSS analysis of the exponents is consistent with the analytical values of the equilibrium 2D Ising model.