论文标题
用于基质蒙特卡洛的特征值弹性算法
Eigenvalue-flipping Algorithm for Matrix Monte Carlo
论文作者
论文摘要
许多物理系统可以用我们通常无法分析的矩阵模型来描述。幸运的是，可以直接地对其进行数字研究。许多常用算法遵循蒙特卡洛方法，该方法对于小基质大小有效，但不能保证与大型矩阵一起工作。在本文中，我们提出了对算法的改进，对于大量的基质模型，它允许以熟练的方式在各种真空之间进行隧道，其中外部提出了特征值的符号变化。我们在两个模型上测试了该方法：纯电势矩阵模型和模糊球体上的标量场理论。
Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.
