论文标题
玻色粒BMN矩阵模型的仿真
Simulations of Bosonic BMN Matrix Model
论文作者
论文摘要
在本论文中，我们提供了通过骨体BMN和骨BFSS矩阵模型的晶格蒙特卡洛模拟获得的结果。使用混合蒙特卡洛（HMC）算法进行模拟。随着系统中温度的变化，BMN矩阵模型有望具有Hagedorn/Deconfinept类型相变。 Polyakov环用作检测相变的顺序参数。除了polyakov循环外，还计算了其他可观察到的诸如内部能量和空间范围之类的主要观测值。我们还通过探索各种相关玩具模型的行为来检查数值模拟算法的有效性。作为本论文的主要结果，我们介绍了使用二小无参数构建的骨气BMN矩阵模型的参数化相图：无量纲的耦合常数和无尺寸温度。
In this thesis we provide the results obtained through lattice Monte Carlo simulations of the bosonic BMN and the bosonic BFSS matrix models. The simulations are performed using Hybrid Monte Carlo (HMC) algorithm. The BMN matrix model is expected to have a Hagedorn/deconfinement type phase transition as the temperature is varied in the system. The Polyakov loop is used as an order parameter for detecting the phase transition. Besides the Polyakov loop, other prime observables such as the internal energy and the extent of space were also computed. We also check the validity of numerical simulation algorithms by exploring the behavior of various relevant toy models. As the main result of this thesis, we present a parametrized phase diagram of the bosonic BMN matrix model constructed using two dimensionless parameters: a dimensionless coupling constant and a dimensionless temperature.
