Abstract
We consider the one-dimensional model of Lieb, Schulz, and Mattis and study the asymptotic behavior of each of the three correlation functions , where , , or . We study in detail the influence of anisotropy by separately studying the correlation functions in both the isotropic and anisotropic cases at both nonzero and zero temperatures. For nonzero temperature we derive both low- and high-temperature expansions for all three correlations and show that these correlations go to zero exponentially as . The behavior near is studied in the isotropic case by considering the limit with fixed, while in the anisotropic case we must hold fixed as . In this manner we obtain the result that if the interaction is stronger in the direction, then approaches a constant exponentially while approaches zero exponentially as . We finally show that in the isotropic case at that . In all cases, at least the first two terms of the asymptotic series are explicitly given.
- Received 12 February 1968
DOI:https://doi.org/10.1103/PhysRev.173.531
©1968 American Physical Society