Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations

Analytic predictions have been derived recently by Dohm and Wessel (2021 Phys. Rev. Lett. 126 060601) from anisotropic phi(4) theory and conformal field theory for the amplitude 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 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 F-c is found to exhibit a nonuniversal dependence on the microscopic couplings of the scalar phi(4) model and the Ising model. Our results are comparedwith the exact result for F-c in the three-dimensional phi(4) model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.

Automated summary

Researchers have verified recent analytic predictions derived from anisotropic phi(4) theory and conformal field theory regarding the critical free energy amplitude of finite anisotropic systems in the two-dimensional Ising universality class through high-precision Monte Carlo simulations, finding remarkable agreement between the experimental data and the theoretical predictions. This study supports the validity of multiparameter universality and refutes the validity of two-scale-factor universality, while also comparing the results with exact results in the three-dimensional phi(4) model with planar anisotropy and briefly discussing the critical Casimir amplitude.