Dynamic behavior of a magnetic system driven by an oscillatory external temperature

The dynamic effects on a magnetic system exposed to a time-oscillating external temperature are studied using Monte Carlo simulations on the classic 2D Ising Model. The time dependence of temperature is defined as $T(t)=T_0 + A \cdot \sin(2\pi t/\tau)$. Magnetization $M(t)$ and period-averaged magnetization $\langle Q\rangle$ are analyzed to characterize out-of-equilibrium phenomena. Hysteresis-like loops in $M(t)$ are observed as a function of $T(t)$. The area of the loops is well-defined outside the critical Ising temperature ($T_c$) but takes more time to close it when the system crosses the critical curve. Results show a power-law dependence of $\langle Q\rangle$ (the averaged area of loops) on both $L$ and $\tau$, with exponents $\alpha=1.0(1)$ and $\beta=0.70(1)$, respectively. Furthermore, the impact of shifting the initial temperature $T_0$ on $\langle Q\rangle$ is analyzed, suggesting the existence of an effective $\tau$-dependent critical temperature $T_c(\tau)$. A scaling law behavior for $\langle Q\rangle$ is found on the base of this $\tau$-dependent critical temperature.