BFSS和IKKT矩阵模型的蒙特卡罗模拟
Monte Carlo Simulations of BFSS and IKKT Matrix Models
摘要：
在这篇论文中，我们使用蒙特卡罗模拟研究了玻色BFSS和IKKT矩阵模型。首先，我们探索了一些玩具模型，以检查数值模拟的有效性。然后，我们模拟了BFSS矩阵模型的哈密顿蒙特卡罗（HMC）算法。在BFSS矩阵模型中，我们使用Polyakov环作为序参量来研究该模型在不同温度下的大N行为。我们的模拟证实，该模型表现出限制-解除限制相变作为系统的温度是不同的。除了Polyakov圈外，还计算了其他观测量，如内能和空间范围。在玻色子IKKT模型中，利用转动惯量张量研究了SO（10）对称性的自发对称性破缺（SSB），发现该模型中不存在SO（10）对称性的自发对称性破缺.除了计算转动惯量张量的本征值外，还计算了其他可观测量，如时空的范围。研究了相位猝灭IKKT模型的仿真理论。
英文摘要：
In this thesis, we studied the bosonic BFSS and IKKT matrix models using Monte Carlo simulations. First, we explored some toy models to check the validity of the numerical simulations. Then we simulated the BFSS matrix model using Hamiltonian Monte Carlo (HMC) algorithm. In the BFSS matrix model, we used the Polyakov loop as an order parameter to investigate the large-N behaviour of this model at different temperatures. Our simulations confirmed that the model exhibits a confinement-deconfinement phase transition as the temperature of the system is varied. Besides the Polyakov loop, other observables such as internal energy and extent of space were also computed. In the bosonic IKKT model, we studied the spontaneous symmetry breaking (SSB) of SO(10) symmetry using the moment of inertia tensor and found that there is no SSB of SO(10) symmetry in this model. Besides the eigenvalues of the moment of inertia tensor, other observable such as extent of spacetime was also computed. We also studied the simulation theory of the phase-quenched IKKT model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
