TY - JOUR
T1 - Asymptotics of Bordered Toeplitz Determinants and Next-to-Diagonal Ising Correlations
AU - Basor, Estelle
AU - Ehrhardt, Torsten
AU - Gharakhloo, Roozbeh
AU - Its, Alexander
AU - Li, Yuqi
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/4
Y1 - 2022/4
N2 - We prove the analogue of the strong Szegő limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk (Physica A 144:44–104, 1987) for the next-to-diagonal correlations ⟨ σ0 , 0σN-1,N⟩ in the 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. We also confirm the leading and subleading terms in an asymptotic formula of Cheng and Wu (Phys Rev 164:719–735, 1967) for ⟨ σ0 , 0σM,N⟩ when M= N and M= N- 1 , thereby establishing the anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.
AB - We prove the analogue of the strong Szegő limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk (Physica A 144:44–104, 1987) for the next-to-diagonal correlations ⟨ σ0 , 0σN-1,N⟩ in the 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. We also confirm the leading and subleading terms in an asymptotic formula of Cheng and Wu (Phys Rev 164:719–735, 1967) for ⟨ σ0 , 0σM,N⟩ when M= N and M= N- 1 , thereby establishing the anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.
KW - Asymptotics
KW - Ising model
KW - Operator Theory
KW - Riemann-Hilbert problems
UR - https://www.scopus.com/pages/publications/85125535489
U2 - 10.1007/s10955-022-02894-7
DO - 10.1007/s10955-022-02894-7
M3 - 文章
AN - SCOPUS:85125535489
SN - 0022-4715
VL - 187
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1
M1 - 8
ER -