A comparative review of recent results on supercritical anomalies in two-dimensional kinetic Ising and Blume–Capel ferromagnets

Following the unexpected experimental discovery of “sideband” peaks in the fluctuation spectrum of thin Co films driven by a slowly oscillating magnetic field with a constant bias (Riego et al. in Phys Rev Lett 118:117202, 2017), numerical studies of two-state Ising and three-state Blume–Capel (BC) ferromagnets in this dynamically supercritical regime have flourished and been successful in explaining this phenomenon. Here, we give a comparative review of this new literature and its connections to earlier work. Following an introduction and a presentation of the two models and the computational method used in many of these studies, we present numerical results for both models. Particular attention is paid to the fact that zero spins in the BC model tend to collect at the interfaces between regions of the two nonzero spin values, ± 1. We present strong arguments that this phenomenon leads to a reduction of the effective interface tension in the BC model, compared to the Ising model. Graphic abstract