论文标题
实际尺度的通用缩放
Universal scaling in real dimension
论文作者
论文摘要
普遍性的概念塑造了我们对多体物理学的理解，但大部分仅限于同质系统。在这里，我们介绍了一项关于非均匀图的普遍性的研究，即远程稀释图（LRDG）。它的缩放理论由单个参数（频谱维度$ d_ {s} $控制），该参数扮演相关参数在复杂几何形状上的作用。所考虑的图表使我们能够连续调整频谱维度的值，并将通用指数作为维数的连续函数找到。通过广泛的数值模拟，我们探测了LRDG上$ O（\ Mathcal {n}）$对称模型的简单实例的缩放指数，显示了定量一致性与真实维度中通用量表的理论预测。
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension $d_{s}$, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously also to noninteger values and to find the universal exponents as continuous functions of the dimension. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of $O(\mathcal{N})$ symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.
