Abstract
A topological interaction method is proposed to study boundary correlation functions and spontaneous magnetization by introducing a topological interaction J to connect spins at two opposite boundaries and by taking the limit J → 0. Conceptual relations between the present scheme and the ghost spin method are discussed. The present paper gives a general starting point for subsequent papers on the applications of the present idea. This method is suggested to be applicable to studying boundary-boundary spin correlations, boundary critical dynamics and non-equilibrium stationary flows. Nonlinear mesoscopic phenomena in infinite systems are quite interesting to study theoretically as well as experimentally. Boundary or surface phase transitions and critical phenomena are still difficult to study rigorously even in low dimensions. A topological treatment is proposed 1) to study spontaneous symmetry breaking (SSB), particularly to calculate the spontaneous magnetization mb at the boundary of the relevant system and boundary-boundary correlation functions. In
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