Analytic predictions have been derived recently by Dohm and Wessel (2021 Phys. Rev. Lett. 126 060601) from anisotropic φ ⁴ theory and conformal field theory for the amplitude 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 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 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 in the three-dimensional φ ⁴ model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.

最近，Dohm 和 Wessel (2021 Phys. Rev. Lett. 126 060601) 从各向异性φ ⁴理论和共形场理论中推导出了二维 Ising 普适性类中有限各向异性系统的临界自由能振幅的分析预测. 这些预测采用了多参数普遍性的假设。我们通过高精度蒙特卡罗 (MC) 模拟测试这些预测方形晶格上的 Ising 模型具有最近邻之间的各向同性铁磁耦合以及沿一条对角线的下一个最近邻之间的各向异性耦合。我们发现 MC 数据和分析预测之间存在显着的一致性。该协议支持多参数普适性的有效性，并使双尺度因子普适性无效，因为发现它表现出对标量φ ⁴模型和 Ising 模型的微观耦合的非普遍依赖性。我们的结果与在球面极限中具有平面各向异性的三维φ ⁴模型中的精确结果进行了比较。简要讨论了临界 Casimir 振幅。