Kinetic Ising model on a two-dimensional additive small-world network under a time-dependent oscillating magnetic field

Dynamic phase transitions in driven magnetic systems represent a fundamental class of nonequilibrium phenomena with rich critical behavior. In this context, we investigate the kinetic Ising model on a two-dimensional additive small-world network (2D A-SWN) under a time-dependent oscillating magnetic field using Monte Carlo simulations with Glauber dynamics. The system consists of a square lattice, where each spin interacts ferromagnetically with its nearest neighbors and additionally couples to one randomly selected distant neighbor, creating a hybrid topology that interpolates between regular and small-world networks. We systematically compute thermodynamic quantities, such as the dynamic order parameter, susceptibility, and the reduced fourth-order Binder cumulant, as a function of the dimensionless parameter Θ, which characterizes the competition between the half-period of the oscillating field and the system’s intrinsic relaxation time. By applying the finite-size scaling theory, we determine the critical exponents associated with the dynamic phase transitions of the system. Our results reveal that the critical exponents do not belong to a clearly defined universality class, suggesting that the long-range interactions in the 2D A-SWN topology induce novel critical behavior in the nonequilibrium dynamic phase transitions, with potential implications for understanding driven systems on complex networks.