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 TTc but also for T⩽Tc. The asymptotic...

We study the two-dimensional Ising model for the square lattice in the presence of a magnetic field which applies on a part of spins. Specifically, we consider the situation in which only the spins on a row or a diagonal line can interact with the magnetic field. The low-temperature series...