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

Abstract

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

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• Critical Casimir Effect: Exact Results
• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice