Analytic predictions have been derived recently by V. Dohm and S. Wessel, Phys. Rev. Lett. {\bf 126}, 060601 (2021) from anisotropic $φ^4$ theory and conformal field theory for the amplitude ${\cal F}_c$ of the critical free energy of finite anisotropic systems in the two-dimensional Ising universality class. These predictions employ the hypothesis of multiparameter universality. We test these predictions by means of high-precision Monte Carlo (MC) simulations for ${\cal F}_c$ of the Ising model on a square lattice with isotropic ferromagnetic couplings between nearest neighbors and with an anisotropic coupling between next-nearest neighbors along one diagonal. We find remarkable agreement between the MC data and the analytical prediction. This agreement supports the validity of multiparameter universality and invalidates two-scale-factor universality as ${\cal F}_c$ is found to exhibit a nonuniversal dependence on the microscopic couplings of the scalar $φ^4$ model and the Ising model. Our results are compared with the exact result for ${\cal F}_c$ in the three-dimensional $φ^4$ model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.
Multiparameter universality and directional nonuniversality of exact anisotropic critical correlation functions of the two-dimensional Ising universality class
Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\geq 2$ Dimensions
将共形场论（CFT）与各向异性$φ^4$理论相结合，导出了$d=2$ Ising普适类中各向异性系统的精确临界Casimir振幅.给出了一般各向异性标量$φ^4$模型和完全各向异性三角格子伊辛模型在有限矩形和无限条几何形状与周期性边界条件（PBC）的显式结果。这些结果证明了受限各向异性系统多参数普适性的有效性和临界Casimir振幅的非普适性。我们发现了一个意想不到的复杂形式的自相似性的各向异性效应附近的不稳定性弱各向异性打破。这可以追溯到$d=2$的各向同性CFT的模不变性。更一般地说，对于$d>2$，我们预测存在的自相似结构的有限尺寸标度功能的$O(n)$对称系统的平面各向异性和PBC的临界区域为$ n \geq 1$，以及在Goldstone为主的低温区域为$ n \geq 2$。
Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid
Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Universität Zürich（苏黎世大学）；Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET（拉普拉塔液体与生物系统物理研究所 (IFLYSIB)，UNLP-CONICET）；Universidad Nacional de La Plata（拉普拉塔国立大学）；ENS de Lyon, CNRS, Laboratoire de Physique（里昂高等师范学校，法国国家科学研究中心，物理实验室）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（美法理论科学中心，法国国家科学研究中心，加州大学圣塔芭芭拉分校KITP）；CNRS, Université de Bordeaux, LOMA, UMR 5798（法国国家科学研究中心，波尔多大学，LOMA联合研究单位5798）
