Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Nat Commun. 2015 Jan 19;6:5968. doi: 10.1038/ncomms6968.
Many physical systems including lattices near structural phase transitions, glasses, jammed solids and biopolymer gels have coordination numbers placing them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. Here we report our investigation of the mechanical instability in a lattice model at finite temperature T. The model we used is a square lattice with a φ(4) potential between next-nearest-neighbour sites, whose quadratic coefficient κ can be tuned from positive to negative. Using analytical techniques and simulations, we obtain a phase diagram characterizing a first-order transition between the square and the rhombic phase and different regimes of elasticity, as well as an 'order-by-disorder' effect that favours the rhombic over other zigzagging configurations. We expect our study to provide a framework for the investigation of finite-T mechanical and phase behaviour of other systems with a large number of floppy modes.
许多物理系统，包括结构相变附近的晶格、玻璃、被堵塞的固体和生物聚合物凝胶，其配位数使它们处于机械不稳定性的边缘。它们的性质取决于软力学模式和热涨落之间的相互作用。在这里，我们报告了我们对有限温度 T 下晶格模型的机械不稳定性的研究。我们使用的模型是一个带有相邻最近邻φ(4)势的正方形晶格，其二次系数 κ 可以从正调至负。我们使用分析技术和模拟，得到了一个相图，该相图描绘了正方形和菱形相之间的一级相变以及不同的弹性区域，以及有利于菱形相对于其他之字形构型的“无序序”效应。我们预计，我们的研究将为研究具有大量软模式的其他系统的有限温度机械和相行为提供一个框架。
