非成对收缩指数矩阵模型的数值和解析研究
Numerical and analytical studies of a matrix model with non-pairwise contracted indices
摘要：
正则张量模型是哈密顿形式中的一种张量模型，可以直接量子化，并具有精确求解的物理状态。状态由具有广义形式的Airy函数的波函数表示。状态的最简单可观测量可以用一个包含非成对指数收缩的矩阵模型表示。这种矩阵模型与将复制技巧应用于自旋玻璃的球形$p$ -自旋模型时出现的模型具有相同的形式，但是我们的情况具有与自旋玻璃情况不同的变量和参数范围。我们分析了矩阵模型解析和数值。我们显示了一些证据的存在下，一个连续的相变的位置所需的一致性条件的正则张量模型。我们还发现在过渡区周围存在着构型的尺度转变。的正则张量模型的结果的影响进行了讨论。
英文摘要：
The canonical tensor model, which is a tensor model in the Hamilton formalism, can be straightforwardly quantized and has an exactly solved physical state. The state is expressed by a wave function with a generalized form of the Airy function. The simplest observable on the state can be expressed by a matrix model which contains non-pairwise index contractions. This matrix model has the same form as the one that appears when the replica trick is applied to the spherical $p$-spin model for spin glasses, but our case has different ranges of variables and parameters from the spin glass case. We analyze the matrix model analytically and numerically. We show some evidences for the presence of a continuous phase transition at the location required by a consistency condition of the canonical tensor model. We also show that there are dimensional transitions of configurations around the transition region. Implications of the results to the canonical tensor model are discussed.
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