论文标题
随机非交通几何形状中的相变
Phase Transition in Random Noncommutative Geometries
论文作者
论文摘要
我们提供了在某些随机非交通几何形状的大$ n $限制中存在相变存在的分析证明。这些几何形状可以表示为狄拉克操作员的合奏。当它们简化为单基质集合时，可以应用库仑气体方法来找到经验光谱分布。我们详细介绍了零零频谱分布的性质。此外，我们表明，这些模型同时表现出一个单一和双切的区域，该区域对于阶参数的某些值，并找到过渡发生的确切值。
We present an analytic proof of the existence of phase transition in the large $N$ limit of certain random noncommutaitve geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix ensembles, one can apply the Coulomb gas method to find the empirical spectral distribution. We elaborate on the nature of the large $N$ spectral distribution of the Dirac operator itself. Furthermore, we show that these models exhibit both a single and double cut region for certain values of the order parameter and find the exact value where the transition occurs.
