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

Dagne Wordofa Tola, Chandan Dasgupta, Mulugeta Bekele

Published 2024-03-10Version 1

We investigate nonequilibrium phase transitions (PTs) in a 2D ferromagnetic Ising model on a square lattice with effective interactions via Monte Carlo (MC) based computational algorithms. Possibly, we simplify the generic complexity of energy function describing the system model to manage the algorithms. The importance of accounting for the effective interactions to admit establishing the nature of nonequilibrium PT emphasizes. The existence of an effective parameter $h$ is verified employing mean-field theory, and the self-consistent equations (SCEs) are derived based on the two familiar dynamics$-$Metropolis and Glauber algorithms. The results qualitatively demonstrate that both dynamics estimate the same SCE for $-1<h<1$. We show the critical temperature $T_{c}$ of the model {\it with} effective interactions to be given as $T_{c}(h\neq 0)=4(1+h)/\ln(3 + 2\sqrt{2})$ where $T_{c}^{0}=T_{c}(h=0)$ retrieves the well-known analytical result of equilibrium Ising model {\it without} the effective interactions. Furthermore, we perform Metropolis MC simulations for a finite system of different lattice sizes with periodic boundary conditions and measure physical quantities of interest. By using data of the measurements, $T_{c}(h)$ and relevant critical { \it exponents} for various values of $h$ are determined employing finite-size scaling (FSS) techniques. The FSS result of $T_{c}(h\neq 0)$ obtained from numerical data is accurately in agreement with analytical results and quite different from $T_{c}^{0}$ as expected. Even so, the numerical results of the exponents are consistent with analytical values of the equilibrium 2D Ising model$-$belonging to the same universality class.