{
  "id": "2102.11561",
  "version": "v1",
  "published": "2021-02-23T09:00:26.000Z",
  "updated": "2021-02-23T09:00:26.000Z",
  "title": "Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations",
  "authors": [
    "Volker Dohm",
    "Stefan Wessel",
    "Benedikt Kalthoff",
    "Walter Selke"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-23T09:00:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal field theory",
      "multiparameter universality",
      "monte carlo simulations",
      "anisotropic confined systems",
      "prediction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}