# Fast algorithm for topologically disordered lattices with constant coordination number

## TL;DR

This paper introduces a fast stochastic algorithm for constructing topologically disordered lattices with constant coordination, improving efficiency over previous methods and demonstrating their relevance in modeling physical systems like amorphous materials.

## Contribution

The paper presents a novel, computationally efficient algorithm for generating constant-coordination disordered lattices, with applications in physics and materials science.

## Key findings

- The algorithm significantly reduces construction time compared to previous methods.
- The 3D Ising model on the CC lattice exhibits a phase transition in the clean Ising universality class.
- Disorder in the CC lattice is non-relevant in the renormalization group sense.

## Abstract

We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier proposal [Phys. Rev. E. 97, 022144 (2018)] 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 non-relevant perturbation in the sense of renormalization group theory.