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DY: Fachverband Dynamik und Statistische Physik

DY 22: Focus Session: Recent Progresses in Criticality in the Presence of Boundaries and Defects I (joint session DY/TT)

DY 22.8: Talk

Wednesday, March 20, 2024, 12:00–12:15, A 151

Quantifying nonuniversal corner free energy contributions in weakly-anisotropic two-dimensional critical systems — •Florian Kischel and Stefan Wessel — RWTH Aachen University, Aachen, Germany

Confined two-dimensional critical systems with corners along the boundary of the spatial domain exhibit a logarithmic contribution to the free energy density. For conformal invariant bulk systems, this corner term has been derived by Cardy and Peschel in terms of the underlying central charge. However, for weakly anisotropic systems, the corner term deviates from this conformal field theory prediction, and the question arises, whether this anisotropy effect can be further quantified in a general way in terms of the asymptotic critical fluctuations. Here, 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 compares well to 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 exected to apply also to other weakly-anisotropic critical two-dimensional systems that allow for a conformal field theory description in the isotropic limit.

Keywords: Criticality with boundaries; conformal field theory; corner free energy; nonuniversality; Ising criticality