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, ' The Suzuki-Trotter formula has been used to get the mth approximant to the classical representation of the partition function of the one-dimensional N-spin 5=+ quantum spin systems. The equivalent two-dimensional (NX2m) Ising model with four-spin interactions has been studied in detail by using the numerically exact transfer-matrix method for T;;;;O.05 and m~8. The convergence properties have been examined in two different representations; checkerboard decomposition (CBD) and real-space decomposition (RSD). The spin correlation functions in RSD converge much faster than those in CBD. The limiting m --+ 00 behavior has been estimated from the extrapolation formula of the form: E( m) = E( 00 ) +a/m 2 • The limiting values of the energy derived from the nearest-neighbor correlation agree with: the correct values excellently.

Study of One-Dimensional Quantum Spin Systems by the Transfer-Matrix Method