论文标题
边界的toeplitz决定因素和近代到对角线相关的渐近学
Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations
论文作者
论文摘要
我们证明了强szeg {\ h o}的类似物限制了一大批边界toeplitz决定因素的定理。 In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations $\langle σ_{0,0}σ_{N-1,N} \rangle$ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the在低温方向上的对角线和水平方面。还建立了近二元相关性的渐近学术语的各向异性依赖性。我们使用Riemann-Hilbert和运营商理论技术独立且并行地证明这些结果。
We 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 $\langle σ_{0,0}σ_{N-1,N} \rangle$ 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.
