TY - JOUR

T1 - Some exact formulae on long-range correlation functions of the rectangular Ising lattice

AU - Chang, Shu Chiuan

AU - Suzuki, Masuo

N1 - Funding Information:
One of the authors (S.-C. C.) would like to thank the support from Nishina Memorial Foundation and Inoue Foundation.

PY - 2004/1/20

Y1 - 2004/1/20

N2 - We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin-spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this mth row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.

AB - We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin-spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this mth row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.

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U2 - 10.1142/S0217979204023842

DO - 10.1142/S0217979204023842

M3 - Article

AN - SCOPUS:1542720546

SN - 0217-9792

VL - 18

SP - 275

EP - 287

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

IS - 2

ER -