Nearestneighbor functions for disordered stealthy hyperuniform manyparticle systems
Abstract
Disordered stealthy manyparticle systems in ddimensional Euclidean space ${\mathbb{R}}^{d}$ are exotic amorphous states of matter that suppress any single scattering events for a finite range of wavenumbers around the origin in reciprocal space. They are currently the subject of intense fundamental and practical interest. We derive analytical formulas for the nearestneighbor functions of disordered stealthy manyparticle systems. First, we analyze asymptotic smallr approximations and expansions of the nearestneighbor functions based on the pseudohardsphere ansatz. We then consider the problem of determining how many of the standard npoint correlation functions are needed to determine the nearest neighbor functions, and find that a finite number suffice. Via theoretical and computational methods, we are able to compare the larger behavior of these functions for disordered stealthy systems to those belonging to crystalline lattices. Such ordered and disordered stealthy systems have bounded hole sizes, and thus compact support for their nearestneighbor functions. However, we find that the approach to the criticalhole size can be quantitatively different, emphasizing the importance of hole statistics in distinguishing ordered and disordered stealthy configurations. We argue that the probability of finding a hole close to the criticalhole size should decrease as a power law with an exponent only dependent on the space dimension d for ordered systems, but that this probability decays asymptotically faster for disordered systems, with either an increase in the exponent of the power law or a crossover into a decay faster than any power law. This implies that holes close to the criticalhole size are rarer in disordered systems. The rarity of observing large holes in disordered systems creates substantial numerical difficulties in sampling the nearest neighbor distributions near the criticalhole size. This motivates both the need for new computational methods for efficient sampling and the development of novel theoretical methods for ascertaining the behavior of holes close to the criticalhole size. We also devise a simple analytical formula that accurately describes these systems in the underconstrained regime for all r. These results provide a theoretical foundation for the analytical description of the nearestneighbor functions of stealthy systems in the disordered, underconstrained regime, and can serve as a basis for analytical theories of material and transport properties of these systems.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 October 2020
 DOI:
 10.1088/17425468/abb8cb
 arXiv:
 arXiv:2009.00123
 Bibcode:
 2020JSMTE2020j3302M
 Keywords:

 random/ordered microstructures;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 41 pages, 17 figures