有限温度U(1)格点规范模型的高阶累积展开之研究

Study of Higher Order Cumulant Expansion of U (1) Lattice Gauge Model at Finite Temperature

在Ｎ＾３σ×Ｎτ（Ｎτ＝１）的高温格点Ｕ（１）模型中，对序参数Ｐｏｌｙａｋｏｖ线＜Ｌ＞作累积展开计算到五级近似，重点在于讨论累积展开在中间耦合区的行动，从累积展开与关联长度的闻系阐明在中间耦合区高阶展开的必要性，采用ｎ级展开对零级展开的修正为零的条件定ｎ级计算中的变分参数，结果显示，不仅在强、弱耦合区，而且在中间耦合区（除了相变点附近）都与蒙特卡罗模拟有较好的符合，随着近似级别的增高。

The order parameter, Polyakov line <L>, of the U(1) gauge model on N_σ~3×N_τ(N_τ=1) lattice by using the cumulant expansion is calculated to the 5-th order. The emphasis is put on the behaviour of the cumulant expansion in the intermediate coupling region. The necessity of higher order expansion is clarified from the connection between the eumulant expansion and the correlation length. The variational parameter in the n-th order calculation is determined by the requirement that corrections of the n-th order expansion to the zeroth order expansion finish. The agreement with the Monte Carlo simulation is obtained not only in the weak and strong coupling regions, but also in the intermediate coupling region except in the very vicinity of the phase transition point.