AI 中文总结
本研究采用伪谱方法求解临界点附近流体的Ornstein-Zernike方程，以平均球近似为封闭条件，得到二维硬核Yukawa粒子的临界指数新结果，还改进了Picard迭代格式，提升了稳定性与收敛速度。
AI 中文摘要
我们采用伪谱方法求解临界点附近模型流体的均匀Ornstein-Zernike（OZ）方程。以平均球近似（MSA）作为OZ方程的封闭条件，针对二维和三维的硬核 Yukawa 粒子系统，获取临界指数η、δ和γ的数值估计。三维MSA的临界指数可通过解析解得到，已为学界熟知，我们的数值方法成功复现了该结果；二维临界指数则是本研究的新成果。伪谱方法能快速、高精度地求解液体态积分方程理论，可处理高度关联态所需的真正无限域计算。此外，我们分析了标准Picard迭代格式，并提出一种变体，该变体可提升迭代的稳定性与收敛速度。
英文摘要
We employ pseudospectral methods to solve the homogeneous Ornstein-Zernike (OZ) equation for a model fluid in the vicinity of the critical point. Focusing on the Mean-Spherical Approximation (MSA) as a closure to the OZ equation, we obtain numerical estimates for the critical exponents $η$, $δ$ and $γ$ for a system of hard-core Yukawa particles both in two and three dimensions. The three-dimensional MSA exponents are already well-known from an analytic solution and are recovered by our numerical methods. The two-dimensional exponents are a new output of this work. The pseudospectral method allows for rapid and highly accurate solution of liquid-state integral equation theories, and enables calculations on truely infinite domains, as needed for highly correlated states. In addition, we analyse the standard Picard iteration scheme and propose a variation of it which provides increased stability and speed of convergence.
