Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.
Phys Rev Lett. 2013 Aug 30;111(9):095503. doi: 10.1103/PhysRevLett.111.095503. Epub 2013 Aug 27.
We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have a vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work, we show that thermal networks exhibit a nonzero shear modulus G well below the isostatic point and that this modulus exhibits an anomalous, sublinear dependence on temperature T. At the isostatic point, G increases as the square root of T, while we find G∝Tα below the isostatic point, where α≃0.8. We show that this anomalous T dependence is entropic in origin.
我们研究了胡克弹性弹簧热网络的弹性性质。在纯力学极限下，当它们的连接性低于临界的等静压值时，这种系统的刚性已知为零。在这项工作中，我们表明，热网络在等静压点以下表现出非零的剪切模量 G，并且该模量表现出异常的、次线性的温度 T 依赖性。在等静压点，G 随 T 的平方根增加，而我们发现 G∝Tα低于等静压点，其中 α≃0.8。我们表明，这种异常的 T 依赖性源于熵。
