论文标题
小$ n $高斯张量模型的实际张量特征值分布的精确分析表达式
Exact analytic expressions of real tensor eigenvalue distributions of Gaussian tensor model for small $N$
论文作者
论文摘要
我们获得了实际张量特征值/矢量分布的精确分析表达式，其对称订单的三个张量张量，带有$ n \ leq 8 $的高斯分布。这是通过明确计算具有四个相互作用的零维玻色剂系统的分区功能来实现的。分布是通过多项式，指数和误差函数的组合作为可行的复杂的肺泡积分的结果来表达的，而复杂的波音积分的结果是在费米子积分后出现的。通过推断表达式并使用先前的结果，我们猜测很大的$ n $表达式。将表达式与蒙特卡洛模拟进行了比较，并分别以确切和大的$ n $表达式获得了精确和良好的一致性。了解集成的可行性将留给未来的研究，这将提供一般的分析公式。
We obtain exact analytic expressions of real tensor eigenvalue/vector distributions of real symmetric order-three tensors with Gaussian distributions for $N\leq 8$. This is achieved by explicitly computing the partition function of a zero-dimensional boson-fermion system with four-interactions. The distributions are expressed by combinations of polynomial, exponential and error functions as results of feasible complicated bosonic integrals which appear after fermionic integrations. By extrapolating the expressions and also using a previous result, we guess a large-$N$ expression. The expressions are compared with Monte Carlo simulations, and precise and good agreement are obtained with the exact and the large-$N$ expressions, respectively. Understanding the feasibility of the integration is left for future study, which would provide a general-$N$ analytic formula.
