Energy Formulation for Infinite Structures: Order Parameter for Percolation, Critical Bonds, and Power-Law Scaling of Contact-Based Transport

Phys Rev Lett. 2024 May 10;132(19):196101. doi: 10.1103/PhysRevLett.132.196101.

Abstract

Investigating heterogeneous materials' microstructure, often simulated using periodic images, is crucial for understanding their physical traits. We propose a generic spring-based representation for periodic two-component structures. The equilibrium energy in this framework serves as an order parameter, offering an analytical expression for wrapping and introducing the concept of critical bonds. We show that these minimum bonds for depercolation can be efficiently detected. The number of critical bonds scales with system size, accurately capturing contact-based transport's scaling. This approach holds potential to analyze functional robustness of networks.