Exact oblique boundary-boundary correlation functions of the two-dimensional ising model

The boundary-boundary correlation in an arbitrary oblique direction for the two-dimensional Ising model is calculated exactly using the topological interaction method. It is shown that these correlation functions satisfy Morita's sum rule not only for T > T-c but also for T <= T-c. The asymptotic form of the oblique boundary-boundary correlation functions is derived. Non-monotonic behaviour of the oblique boundary-boundary correlation functions with respect to the system-size is found by using numerical calculations of an exact integral representation of the oblique correlation. (c) 2005 Elsevier B.V. All rights reserved.