论文标题
一维$ ϕ^4 $晶格模型的投射截断 - 符号抗性研究
Projective-truncation-approximation study of the one-dimensional $ϕ^4$ lattice model
论文作者
论文摘要
在本文中，我们首先为经典统计模型的绿色运动功能方程（EOM）形式主义中的射击截断近似（PTA）开发。为了为给定的哈密顿量实施PTA，我们选择一组基础变量并投影截断了层次EOM。我们将PTA应用于一维$ ϕ^4 $晶格型号。详细研究了声子分散和静态相关函数。使用一维碱基，我们分别获得与二次变异近似相同的结果。特别是，我们分析了低温和高温极限中静态平均值的幂律温度依赖性，并给出了确切的指数。
In this paper, we first develop the projective truncation approximation (PTA) in the Green's function equation of motion (EOM) formalism for classical statistical models. To implement PTA for a given Hamiltonian, we choose a set of basis variables and projectively truncate the hierarchical EOM. We apply PTA to the one-dimensional $ϕ^4$ lattice model. Phonon dispersion and static correlation functions are studied in detail. Using one- and two-dimensional bases, we obtain results identical to and beyond the quadratic variational approximation, respectively. In particular, we analyze the power-law temperature dependence of the static averages in the low- and high-temperature limits, and we give exact exponents.
