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>Tc but also for T⩽Tc. 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.