The topological interaction method is applied to the evaluation of boundary-boundary correlation functions, which yield the square of the spontaneous magnetization m b at the boundary in the thermodynamic limit. One of the remarkable results is that the boundary-boundary correlation function C M is found to be nonmonotonic with respect to the system size M for T< T c, because of boundary effects. On the other hand, it is monotonic above T c, C M ≃(A +(T) √M) exp(-M/ξ) with the correlation length f and with A +(T) ~ √T-T c near the critical point T c. At the critical point, C M~1/M, and below T c, C M=m b 2+(-A_(T)√M +B(T) + C(T)√M)exp(-M/ξ), where A_(T)~m b 3, B(T)~m b 3, C(T)~m b√T-T c. Fisher's finite-size scaling is confirmed in this respect.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics