Nonequilibrium phase transitions in a 2D ferromagnetic spins with effective interactions

Abstract 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 (PTs) in a two-dimensional (2D) ferromagnetic Ising model on a square lattice under effective interactions using Monte Carlo (MC) algorithms. It requires extensive MC simulations using the modified Metropolis and Glauber update rules. Using an appropriate definition of an effective parameter h helps to qualify the modified update rules. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the analytical solution shows that the nature of the PT (including the critical temperature) is independent of h . Furthermore, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>h</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , we study the steady-state properties of PTs 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.