标题： 二维伊辛模型的非守恒临界动力学作为表面动力粗糙化过程 显示英文标题

标题： Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process

摘要： 我们通过数值模拟二维伊辛模型的格点和连续形式——Glauber动力学和时间依赖的Ginzburg-Landau（TDGL）方程——重新研究了非守恒（或模型A）临界动力学，以利用表面动力学粗化的当前工具进行分析。 我们的研究考察了两种临界淬火，一种是从有序初始状态，另一种是从无序初始状态，对于这两种情况，我们评估了动态标度假设、临界指数值以及出现的涨落场统计。 值得注意的是，系统遵循的动态标度假设强烈依赖于初始条件：从有序相进行的临界淬火遵循Family-Vicsek（FV）标度，而从无序相进行的临界淬火则表现出初始过度生长阶段的内在异常粗糙化，随后趋于平衡。 这种行为可以通过临界温度下随机Ginzburg-Landau方程的动力学不稳定性来解释，其中线性不稳定的项最终由非线性相互作用稳定。 对于这两种淬火，我们确定了场涨落的概率分布函数，在适当用随时间变化的涨落幅度归一化后，这些分布函数在非平衡动力学过程中是时间不变的。 此外，我们开发了一个相关的界面模型，该模型中的场与TDGL场的空间积分成比例（积分GL模型）。 对该模型的数值模拟揭示了FV或棱面异常粗糙化，具体取决于所进行的临界淬火，以及从有序相进行的临界淬火中涨落统计的涌现对称性。 显示英文摘要

摘要： We have revisited the non-conserved (or model A) critical dynamics of the two-dimensional Ising model through numerical simulations of its lattice and continuum formulations --Glauber dynamics and the timedependent Ginzburg-Landau (TDGL) equation, respectively--, to analyze them with current tools from surface kinetic roughening. Our study examines two critical quenches, one from an ordered and a different one from a disordered initial state, for both of which we assess the dynamic scaling ansatz, the critical exponent values, and the fluctuation field statistics that occur. Notably, the dynamic scaling ansatz followed by the system strongly depends on the initial condition: a critical quench from the ordered phase follows Family-Vicsek (FV) scaling, while a critical quench from the disordered phase shows an initial overgrowth regime with intrinsic anomalous roughening, followed by relaxation to equilibrium. This behavior is explained in terms of the dynamical instability of the stochastic Ginzburg-Landau equation at the critical temperature, whereby the linearly unstable term is eventually stabilized by nonlinear interactions. For both quenches we have determined the occurrence of probability distribution functions for the field fluctuations, which are time-independent along the non-equilibrium dynamics when suitably normalized by the time-dependent fluctuation amplitude. Additionally, we have developed a related interface model for a field which scales as the space integral of the TDGL field (integral GL model). Numerical simulations of this model reveal either FV or faceted anomalous roughening, depending on the critical quenched performed, as well as an emergent symmetry in the fluctuation statistics for a critical quench from the ordered phase.