CHE Hao, XIA Yu, WANG Hong-mo, SONG Yong-xin
理论物理通讯. 1989, 12(3): 273-289.
The standard variational-cumulant expansion (VC) combined with a scheme for the enumeration of connected diagrams is employed to study the simple Ising model with the second-order phase transition. This model is evaluated to the 5th order approximations. A comparison with the 2-dimensional exact results shows that thermodynamic quantities converge rather slowly to the exact values in the intermediate region. A strict analytical calculation of the critical temperature with the 5th order approxinlation both for Ji and cumulant expansion suggests that VC chn achieve rather high standard accuracy if the variational parameters Ji could be determined up to higher degrees of corrections rather than the first one. Anomalies are found for U, C and M at extremely low temperature. A detailed study of M implies that thermodynamic formulae should be carefully chosen in VC approach so as to avoid these anomalies.