Basor, EstelleEhrhardt, TorstenGharakhloo, RoozbehIts, AlexanderLi, Yuqi2022-03-212022-03-212021Basor, E., Ehrhardt, T., Gharakhloo, R., Its, A., & Li, Y. (2021). Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations. ArXiv:2011.14561 [Math-Ph]. https://doi.org/10.48550/arXiv.2011.14561https://hdl.handle.net/1805/28215We prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations ⟨σ0,0σN−1,N⟩ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the diagonal and horizontal ones in the low temperature regime. The anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations is also established. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.enAttribution 4.0 Internationalbordered Toeplitz determinantsasymptoticsArticle