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

• Published in: arXiv.org 2021-06
• Main Authors: Dohm, Volker, Wessel, Stefan, Kalthoff, Benedikt, Selke, Walter
• Format: Article
• Language: English
• Subjects: Amplitudes; Anisotropy; Couplings; Ferromagnetism; Field theory; Free energy; Ising model; Three dimensional models
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2102.11561

Analytic predictions have been derived recently by V. Dohm and S. Wessel, Phys. Rev. Lett. {\bf 126}, 060601 (2021) from anisotropic \(\varphi^4\) 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 \(\varphi^4\) model and the Ising model. Our results are compared with the exact result for \({\cal F}_c\) in the three-dimensional \(\varphi^4\) model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.