TY - JOUR

T1 - Study on boundary-boundary correlation functions of the two-dimensional Ising model using topological interaction method

AU - Suzuki, Masuo

AU - Suzuki, Hidenori

AU - Chang, Shu Chiuan

N1 - Funding Information:
One of the authors (S.-C. C.) would like to thank the support from Nishina Memorial Foundation, Inoue Foundation and National Center for Theoretical Sciences at Taipei.

PY - 2005/3

Y1 - 2005/3

N2 - 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.

AB - 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.

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U2 - 10.1063/1.1845954

DO - 10.1063/1.1845954

M3 - Article

AN - SCOPUS:17744367874

SN - 0022-2488

VL - 46

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

M1 - 033301

ER -