Spin-spin correlators on the β/β^ boundaries in 2D Ising-like models: non-universality in the scaling region

In this work, we investigate quantitative properties of correlation functions on the boundaries between two 2D Ising-like models with dual parameters β and β^. Spin-spin correlators in such constructions without reflection symmetry with respect to transnational-invariant directions are usually represented as 2× 2 block Toeplitz determinants which are normally significantly harder than the scalar (1× 1-blocked) versions. Nevertheless, we show that for the specific β/β^ boundaries considered in this work, the symbol matrices allow explicit commutative Wiener-Hopf factorizations. However, the Wiener-Hopf factors at different z do not commute. We will show that due to this non-commutativity, "logarithmic divergences" and non-universal short distance contributions in the Wiener-Hopf factors fail to factorize out completely in the re-scaled correlators. This leads to non-universality of the leading large r asymptotics at the order e⁻ʳr3/2, even when the constant terms are re-scaled to be the same.