Gregorio Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E. 2017 Dec;96(6-1):062147. doi: 10.1103/PhysRevE.96.062147. Epub 2017 Dec 28.
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.
我们分析了一个一维的自旋弦模型，其中弦振荡器与它们的两个最近邻以及代表内部自由度的伊辛自旋线性耦合。弦-自旋耦合诱导了自旋之间的长程铁磁相互作用，与自旋-自旋反铁磁耦合竞争。因此，系统的复杂相图表现出不同的平纹和褶皱状态，状态之间有一级或二级相变线。这种复杂性转化为模型的二维版本，其数值解最近被用于定性地解释在悬栅石墨烯片的扫描隧道显微镜实验中观察到的从波纹到褶皱的转变。在这里，我们使用分岔理论详细描述了更简单的一维模型的相图和相稳定性。这为不同相的物理机制以及实验中观察到的行为提供了更多的见解。
