Fast algorithm for topologically disordered lattices with constant coordination number

Abstract

We present a stochastic algorithm for constructing a topologically disordered (i.e., nonregular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier proposal [Schrauth, Richter, and Portela, Phys. Rev. E 97, 022144 (2018)2470-004510.1103/PhysRevE.97.022144] with respect to both computational complexity and finite-size scaling properties-making the CC lattice an alternative to proximity graphs which, especially in higher dimensions, is significantly faster to build. Among other applications, physical systems such as certain amorphous materials with low concentration of coordination defects are an important example of disordered, constant-coordination lattices in nature. As a concrete application, we characterize the criticality of the 3D Ising model on the CC lattice. We find that its phase transition belongs to the clean Ising universality class, establishing that the disorder present in the CC lattice is a nonrelevant perturbation for this model in the sense of renormalization group theory.