标题： 通过分区函数零点的相变性质：重新审视Blume-Capel铁磁体 显示英文标题

标题： Phase transition properties via partition function zeros: The Blume-Capel ferromagnet revisited

摘要： 自Lee和Yang的开创性工作以来，在复数磁场平面上定位分区函数的零点已成为研究相变的强大方法。 Fisher后来将这种方法扩展到复数温度，随后的推广引入了其他控制参数，例如晶体场。 在以前的工作中[Moueddene等人，J. Stat. Mech. (2024) 023206；Phys. Rev. E 110, 064144 (2024)]，我们将这一框架应用于二维和三维Blume-Capel模型——一个具有丰富相结构的系统，其中二级临界线在三临界点与一级线相交。 我们表明，Lee-Yang、Fisher和晶体场零点的标度可以准确地得到临界指数，即使对于中等晶格尺寸也是如此。 在本研究中，我们扩展了这一分析，并证明无需在名义上的相变点进行模拟即可获得可靠的指数估计。 引人注目的是，小系统尺寸就足够了，这不仅提高了方法效率，还推进了减少大规模计算研究碳足迹的更广泛目标。 显示英文摘要

摘要： Since the landmark work of Lee and Yang, locating the zeros of the partition function in the complex magnetic-field plane has become a powerful method for studying phase transitions. Fisher later extended this approach to complex temperatures, and subsequent generalizations introduced other control parameters, such as the crystal field. In previous works [Moueddene et al, J. Stat. Mech. (2024) 023206; Phys. Rev. E 110, 064144 (2024)] we applied this framework to the two- and three-dimensional Blume-Capel model -- a system with a rich phase structure where a second-order critical line meets a first-order line at a tricritical point. We showed that the scaling of Lee-Yang, Fisher, and crystal-field zeros yields accurate critical exponents even for modest lattice sizes. In the present study, we extend this analysis and demonstrate that simulations need not be performed exactly at the nominal transition point to obtain reliable exponent estimates. Strikingly, small system sizes are sufficient, which not only improves methodological efficiency but also advances the broader goal of reducing the carbon footprint of large-scale computational studies.