Finite temperature mechanical instability in disordered lattices

Leyou Zhang; Xiaoming Mao

doi:10.1103/physreve.93.022110

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arXiv · 1503.05274

Finite temperature mechanical instability in disordered lattices

Leyou Zhang·Xiaoming Mao

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Abstract

Mechanical instability takes different forms in various ordered and disordered systems. We study the effect of thermal fluctuations in two disordered central-force lattice models near mechanical instability: randomly diluted triangular lattice and randomly braced square lattice. These two lattices exhibit different scalings for the emergence of rigidity at $T=0$ due to their different patterns of self stress at the transition. Using analytic theory we show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as $G \sim T^{1/2}$, whereas the square lattice shows $G \sim T^{2/3}$.

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Leyou Zhang, Xiaoming Mao. 2015-03-18. Finite temperature mechanical instability in disordered lattices. https://doi.org/10.1103/physreve.93.022110

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