Jack Robert L, Berthier Ludovic
Department of Physics, University of Bath, Bath, BA2 7AY, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021120. doi: 10.1103/PhysRevE.85.021120. Epub 2012 Feb 15.
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localization in a single state. At low temperatures, both models exhibit scaling behavior. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group treatments.
我们使用一种随机钉扎程序来研究两种玻璃态自旋模型中的非晶序。在恒温下增加钉扎自旋的浓度时，我们发现从体弛豫到单个状态的局域化存在一个急剧的转变（但没有热力学相变）。在低温下，两种模型都表现出标度行为。我们讨论了与非晶序相关的不断增长的长度和时间尺度，以及将系统局域化到单个状态所需的钉扎自旋分数。这些针对有限维相互作用模型获得的结果，为随机钉扎效应提供了一种理论情形，该情形与先前基于平均场、模式耦合或重整化群处理的方法在定性上有所不同。
