Quantifying nonuniversal corner free-energy contributions in weakly anisotropic two-dimensional critical systems

We derive an exact formula for the corner free-energy contribution of weakly anisotropic two-dimensional critical systems in the Ising universality class on rectangular domains, expressed in terms of quantities that specify the anisotropic fluctuations. The resulting expression agrees with numerical exact calculations that we perform for the anisotropic triangular Ising model and quantifies the nonuniversality of the corner term for anisotropic critical two-dimensional systems. Our generic formula is expected to apply also to other weakly-anisotropic critical two-dimensional systems that allow for a conformal field theory description in the isotropic limit. We consider the three-states and four-states Potts models as further specific examples.