## Abstract

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.

Original language | English |
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Article number | 033301 |

Journal | Journal of Mathematical Physics |

Volume | 46 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Mar |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics