  We investigate nonequilibrium phase transitions in a 2D ferromagnetic Ising
model on a square lattice with effective interactions using Monte Carlo-based
computational algorithms. We verify the effective parameter $h$ by employing
mean-field theory and derive self-consistent equations (SCEs) using two
familiar dynamics: Metropolis and Glauber. For $-1<h<1$, both dynamics are
expected to estimate the same SCE. We find the relation between $T_{c}$ and
$T_{c}^{0}$ where $T_{c}$ ($T_{c}^{0}$) is the critical temperature of the
model with (without) the effective interactions. Here, $T_{c}^{0}$ refers to
the well-known analytical result of the equilibrium Ising model. We perform the
simulations for different lattice sizes that enable us to measure physical
quantities of interest. From numerical data, we determine $T_{c}$ and relevant
exponents for various values of $h$ by employing finite-size scaling (FSS). We
find that the FSS result of $T_{c}$, which is quite different from $T_{c}^{0}$,
is in agreement with that of its analytical result, and the accuracy is good
regardless of the types of model. The numerical results of the exponents are
consistent with the analytical values of the equilibrium 2D Ising model, which
belongs to the same universality class.
