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arXiv · 2102.11561

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

Volker Dohm·Stefan Wessel·Benedikt Kalthoff·Walter Selke
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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.

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Volker Dohm, Stefan Wessel, Benedikt Kalthoff, Walter Selke. 2021-02-23. Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations. https://doi.org/10.1088/1751-8121%2Fabf7f8

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