Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions

The two-point correlations formed by spin and energy-density operators are calculated exactly for the semi-infinite two-dimensional Ising model. It is shown that these correlations have a scaling form near the critical point. The asymptotic behaviour of the scaling functions is studied for various distances and configurations of operators on the lattice. The results obtained are used for the verification of the phenomenological theories: the decay of correlations and scaling. On the basis of the exact results the phenomenological rule for calculating the asymptotics of the correlation functions is proposed for the case when the distance between one of the operators and the boundary is much smaller than the distance between the operators. Using this rule, the dependence of the local thermodynamic functions on the distance from the boundary is obtained.