Universal Finite Size Scaling Amplitudes in Two Dimensional Critical Phenomena.

We study the φ 4 lattice model with anisotropic short-range interactions. We show that the nonuniversal finite-size scaling functions of the anisotropic φ 4 model in a d -dimensional rectangular geometry are determined by the universal finite-size scaling functions of the isotropic φ 4 theory in a d -dimensional parallelepiped. Predictions are made for the Binder cumulant. In the bulk limit two-scale factor universality is absent in those universal critical-point amplitude relations that involve the correlation length.We study the φ 4 lattice model with anisotropic short-range interactions. We show that the nonuniversal finite-size scaling functions of the anisotropic φ 4 model in a d -dimensional rectangular geometry are determined by the universal finite-size scaling functions of the isotropic φ 4 theory in a d -dimensional parallelepiped. Predictions are made for the Binder cumulant. In the bulk limit two-scale factor universality is absent in those universal critical-point amplitude relations that involve the correlation length.

Journal of Physics A Mathematical and GeneralApr 19, 200617 citations

Universal finite-size scaling around tricriticality between topologically ordered, symmetry-protected topological, and trivial phases

Ke Wang, Tigran Sedrakyan

Quantum one-dimensional criticality with conformal invariance is known to be characterized by conformal field theory with the inherent central charge ( $c$ ), and universal finite-size amplitudes. Here, the authors demonstrate that around a quantum criticality with $c$ =\textonehalf{} and two Majorana boundary modes, the symmetry-breaking effect modifies the finite-size amplitudes from a universal constant to be a universal function of an emergent scale. This finding provides a new perspective to study the interplay of topology and quantum criticality.Quantum one-dimensional criticality with conformal invariance is known to be characterized by conformal field theory with the inherent central charge ($c$), and universal finite-size amplitudes. Here, the authors demonstrate that around a quantum criticality with $c$=\textonehalf{} and two Majorana boundary modes, the symmetry-breaking effect modifies the finite-size amplitudes from a universal constant to be a universal function of an emergent scale. This finding provides a new perspective to study the interplay of topology and quantum criticality.

arXiv:1911.01512Physical review. B./Physical review. BJan 10, 20207 citations

Finite Size Effects in Critical Phenomena.

Jia Liang Han

Jan 1, 19870 citations

Quantum one-dimensional criticality with conformal invariance is known to be characterized by conformal field theory with the inherent central charge (

c

), and universal finite-size amplitudes. Here, the authors demonstrate that around a quantum criticality with

c

=\textonehalf{} and two Majorana boundary modes, the symmetry-breaking effect modifies the finite-size amplitudes from a universal constant to be a universal function of an emergent scale. This finding provides a new perspective to study the interplay of topology and quantum criticality.