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...

The topological interaction method proposed by Suzuki is applied to the transverse Ising chain and XY chain in order to study the behaviour of the boundary–boundary correlations. The correlation function 〈σ1xσNx〉 for the thermodynamic limit is derived by this method as a function of the...

The magnetization and the electron number at the edge site are analytically calculated in the repulsive Hubbard model with a small magnetic field near the half-filling. Such quantities in the strong-coupling limit are evaluated. The relationship between the repulsive and the attractive Hubbard...