发表机构
Beijing University of Posts and Telecommunications; Beijing Institute of Technology（北京邮电大学; 北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过蒙特卡罗模拟和有限尺寸标度，研究方格上各向异性三态Potts模型，发现各向异性仅改变有效临界几何，不改变普适类，并用理论纵横比恢复方向等价性。
AI 中文摘要
我们利用Wolff单簇蒙特卡罗模拟和有限尺寸标度研究了方格上的二维各向异性三态Potts铁磁体。对于耦合比λ=J_y/J_x=0.5、0.75和1，关联比的有限尺寸标度给出了与二维三态Potts普适类一致的临界行为。领先Fisher零点的标度给出与ν=5/6一致的关联长度指数，而其累积密度与预期的比热指数α=1/3一致。我们进一步利用方向性关联比R_x和R_y以及方向性FK缠绕概率来表征临界各向异性。对于物理方格上的λ=0.5，R_x和R_y趋近于不同的临界值，同时给出共同的关联长度指数。从缠绕概率中，我们独立确定了有效纵横比ρ_e^□=0.6413(5)，与从等径向表示获得的理论值ρ_e^{□,th}≃0.64150030非常接近。利用理论值设定物理纵横比恢复了方向等价性，R_x≃R_y，并使整体关联比趋向各向同性方格参考值。结果表明，空间各向异性改变了有效临界几何，而不改变体三态Potts普适类。
英文摘要
We study the two-dimensional anisotropic three-state Potts ferromagnet on the square lattice using Wolff single-cluster Monte Carlo simulations and finite-size scaling. For coupling ratios $λ=J_y/J_x=0.5$, $0.75$, and $1$, finite-size scaling of the correlation ratio yields critical behavior consistent with the two-dimensional three-state Potts universality class. The scaling of the leading Fisher zeros gives a correlation-length exponent consistent with $ν=5/6$, while their cumulative density is consistent with the expected specific-heat exponent $α=1/3$. We further characterize the anisotropy at criticality using directional correlation ratios $R_x$ and $R_y$ together with directional FK wrapping probabilities. For $λ=0.5$ on a physically square lattice, $R_x$ and $R_y$ approach distinct critical values while yielding a common correlation-length exponent. From the wrapping probabilities, we independently determine an effective aspect ratio $ρ_e^\square=0.6413(5)$, in close agreement with the theoretical value $ρ_e^{\square,\mathrm{th}}\simeq0.64150030$ obtained from the isoradial representation. Using the theoretical value to set the physical aspect ratio restores directional equivalence, $R_x\simeq R_y$, and brings the overall correlation ratio toward the isotropic-square reference. The results show that spatial anisotropy changes the effective critical geometry without altering the bulk three-state Potts universality class.
Comments9 pages,5 figures
