2015/03/18 by Leyou Zhang, Xiaoming Mao · 18 citations
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Geometry #Hexagonal lattice #High-pressure geophysics and materials #Instability #Lattice (music) #Material Dynamics and Properties #Mathematical physics #Mathematics #Mechanics #Physics #Quantum mechanics #Renormalization group #Rigidity (electromagnetism) #Scaling #Shear modulus #Square lattice #Statistical physics #Theoretical and Computational Physics #Thermal #Thermal fluctuations #Thermodynamics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.93.022110
published in Physical review. E 93(2), 022110 (American Physical Society) · 8 pages, 3 figures
arxiv created 2015/03/18 · openalex publication_date 2016/02/08 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.