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

TL;DR

This study tests recent theoretical predictions about the critical free energy of anisotropic 2D Ising systems using high-precision Monte Carlo simulations, confirming multiparameter universality and challenging two-scale-factor universality.

Contribution

The paper provides the first high-precision numerical validation of multiparameter universality predictions for anisotropic systems in the 2D Ising universality class.

Findings

Monte Carlo data agree with analytical predictions

Supports validity of multiparameter universality

Shows nonuniversal dependence of ${\

Abstract

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.