Beschreibung:
<jats:title>Abstract</jats:title>
<jats:p>Analytic predictions have been derived recently by Dohm and Wessel (2021 <jats:italic>Phys. Rev. Lett.</jats:italic>
<jats:bold>126</jats:bold> 060601) from anisotropic <jats:italic>φ</jats:italic>
<jats:sup>4</jats:sup> theory and conformal field theory for the amplitude <jats:inline-formula>
<jats:tex-math><?CDATA ${\mathcal{F}}_{\mathrm{c}}$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aabf7f8ieqn1.gif" xlink:type="simple" />
</jats:inline-formula> 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 <jats:inline-formula>
<jats:tex-math><?CDATA ${\mathcal{F}}_{\mathrm{c}}$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aabf7f8ieqn2.gif" xlink:type="simple" />
</jats:inline-formula> 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 <jats:inline-formula>
<jats:tex-math><?CDATA ${\mathcal{F}}_{\mathrm{c}}$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aabf7f8ieqn3.gif" xlink:type="simple" />
</jats:inline-formula> is found to exhibit a nonuniversal dependence on the microscopic couplings of the scalar <jats:italic>φ</jats:italic>
<jats:sup>4</jats:sup> model and the Ising model. Our results are compared with the exact result for <jats:inline-formula>
<jats:tex-math><?CDATA ${\mathcal{F}}_{\mathrm{c}}$?></jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll">
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="aabf7f8ieqn4.gif" xlink:type="simple" />
</jats:inline-formula> in the three-dimensional <jats:italic>φ</jats:italic>
<jats:sup>4</jats:sup> model with a planar anisotropy in the spherical limit. The critical Casimir amplitude is briefly discussed.</jats:p>