AI 中文总结
研究二维伊辛模型向平衡态的弛豫行为，通过有限尺寸效应产生的缩放关系估计自相关指数\(\lambda\)和动力学指数\(z\)，并将光滑畴壁类似晶格边界处理，扩展假设到非平衡系统。
AI 中文摘要
研究了具有最近邻相互作用的二维伊辛模型向平衡态的弛豫行为，重点关注二次自相关函数\(C(t,s)\)。影响增长磁畴的有限尺寸效应导致\(C(t,s)\)饱和，其具有高度为\(C_{\infty}^{(2)}(s,L)\)的明显平台，该平台随等待时间\(s\)和晶格尺寸\(L\)代数缩放。利用这些缩放关系，通过故意使用小晶格来精确估计自相关指数\(\lambda\)和动力学指数\(z\)。将光滑畴壁与晶格边界类似处理，其对\(C(t,s)\)的影响可理解为过早的有限尺寸现象，将假设扩展到尚未达到平衡的系统。
英文摘要
The relaxation behavior towards equilibrium of the $2D$ Ising model with nearest-neighbor interactions has been studied with focus on the two-time autocorrelator $C(t,s)$. Finite-size effects affecting the growing magnetic domains lead to the saturation of $C(t,s)$ with a distinct plateau of height $C_{\infty}^{(2)}(s,L)$ scaling algebraically with waiting time $s$ and lattice size $L$. These scaling relations are used to produce precise estimates for the autocorrelation exponent $λ$ and dynamical exponent $z$ with deliberately small lattices. Treating smooth domain walls in a similar manner to the lattice boundaries, their effect on $C(t,s)$ can be understood as premature finite-size phenomenon, extending our ansatz to systems not yet in equilibrium.
Comments18 pages, 16 figures; changes: minor grammar revisions, inclusion of lambda^* estimates in text, hyperlinks of ISBNs to DOIs, minor corrections in Refs
Journal refDustin Warkotsch et al J. Stat. Mech. (2026) 073208
