We give some examples to illustrate that scale invariance may not be a manifestation of complex behavior in one-dimensional sandpile models. The multiscaling statistical properties and the existence of intrinsic length scales observed in the local limited one-dimensional model reflects a certain level of complexity. The local, limited, and limited to no traps model presents scale invariance due to the inhomogeneous way of perturbing the lattice. It behaves, however, as the trivial one-dimensional version of the Bak, Tang, and Wisenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] model. A nonlocal limited model presents scaling statistical properties and displays the same level of complexity as the nontrivial two-dimensional models.
展开▼
机译：我们提供一些示例来说明尺度不变性可能不是一维沙堆模型中复杂行为的体现。在局部有限一维模型中观察到的多尺度统计特性和固有长度尺度的存在反映了一定程度的复杂性。由于扰动晶格的方式不统一，局部，有限和无陷阱模型呈现出尺度不变性。然而，它表现为Bak，Tang和Wisenfeld的琐碎的一维版本[Phys。牧师59，381（1987）;物理Rev. A 38，364（1988）]模型。非局部受限模型呈现缩放统计属性，并显示与非平凡二维模型相同的复杂度。
展开▼
