AI 中文总结
该研究针对周期性磁驱动的二维伊辛模型，推导了含时周期性均匀源作用下的动态标度变量，揭示了磁化强度等的振荡标度行为，并简要探讨了零磁场下温度周期驱动伊辛系统的动态特性。
AI 中文摘要
我们研究与序参量场耦合的含时周期性均匀源所产生的临界动力学，该源驱动经典铁磁系统跨越连续相变。为此，我们考虑处于周期性磁场$h(t)=-A\cos(2\pi t/P)$中的典型二维（2D）伊辛模型，该模型在临界温度下按纯弛豫动力学演化。我们表明，周期性驱动在热力学极限下会产生一种特殊的动态标度行为，这种行为源于时间$t$、$h(t)$的振幅$A$与周期$P$之间的非平凡相互作用。相关的标度变量为$\tau=t/P$和$\sigma=A P^\kappa$，其中$\kappa = y_h/z$，$y_h=(d+2-\eta)/2$是磁场的临界维度，$z$是临界弛豫动力学的动态指数（对于二维伊辛模型，$\kappa\approx0.865$）。磁化强度和键能密度的动态标度行为表现为围绕一条平滑曲线的振荡，该曲线趋近于大$\tau$下的稳态行为。我们还简要讨论了零磁场下，由随时间周期性变化的温度驱动跨越临界点的伊辛系统的动态行为。
英文摘要
We study the critical dynamics arising from a time-dependent periodic homogenous source coupled to the order-parameter field, which drives a classical ferromagnetic system across a continuous transition. For this purpose, we consider the paradigmatic two-dimensional (2D) Ising model in the presence of a periodic magnetic field $h(t)=-A\, \cos (2πt/P)$, evolving under a purely relaxational dynamics at the critical temperature. We show that the periodic driving gives rise to a peculiar dynamic scaling behavior in the thermodynamic limit, arising from a nontrivial interplay among the time $t$, the amplitude $A$ and period $P$ of $h(t)$. The relevant scaling variables are $τ=t/P$ and $σ=A P^κ$, with $κ= y_h/z$, where $y_h=(d+2-η)/2$ is the critical dimension of the magnetic field, and $z$ is dynamic exponent for the critical relaxational dynamics ($κ\approx 0.865$ for the 2D Ising model). The dynamic scaling behaviors of the magnetization and bond-energy density show an oscillatory behavior around a smooth curve which approaches a large-$τ$ stationary behavior. We also briefly discuss the dynamic behavior of an Ising system driven across the critical point by a periodic time-varying temperature at zero magnetic field.
Comments13 pages
