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arXiv 1503.05274cond-mat.softcond-mat.dis-nncond-mat.mtrl-scicond-mat.stat-mech
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无序晶格中的有限温度力学不稳定性

Finite temperature mechanical instability in disordered lattices

Leyou Zhang, Xiaoming Mao

摘要:

在各种有序和无序系统中,力学不稳定性表现为不同的形式。本文研究了两种无序中心力晶格模型:随机稀释三角晶格和随机支撑正方晶格中的热涨落效应。这两种晶格在$T=0$处出现刚性时表现出不同的标度,这是由于它们在过渡处的自应力模式不同。使用解析理论,我们表明,热波动稳定两个晶格。特别地,三角形晶格显示出剪切模量按$G \sim T^{1/2}$缩放的临界状态,而正方形晶格显示出$G \sim T^{2/3}$。

英文摘要:

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 $G \sim T^{2/3}$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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