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

Abstract

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.