Celeste Mendes | Searcharxiv

arXiv2025

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 [P.~Riego et al., 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 he 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.

cond-mat.stat-mech↗

arXiv2024

Numerical Simulation of a Two-Dimensional Blume-Capel Ferromagnet in an Oscillating Magnetic Field with a Constant Bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of $\pm 1, 0$, with a non-zero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multi-droplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model . Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.

cond-mat.stat-mech↗