Ibrahim Ahmed K, Barghathi Hatem, Vojta Thomas
Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042132. doi: 10.1103/PhysRevE.90.042132. Epub 2014 Oct 21.
We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally in the active phase while the bulk system is still in the inactive phase. Specifically, if the correlations decay as a power of the distance, the rare-region probability is a stretched exponential of the rare-region size rather than a simple exponential as is the case for uncorrelated disorder. As a result, the Griffiths singularities are enhanced and take a non-power-law form. The critical point itself is of infinite-randomness type but with critical exponent values that differ from the uncorrelated case. We report large-scale Monte Carlo simulations that verify and illustrate our theory. We also discuss generalizations to higher dimensions and applications to other systems such as the random transverse-field Ising model, itinerant magnets, and the superconductor-metal transition.
我们研究了存在长程空间无序关联时无序接触过程中的非平衡相变。这些关联极大地增加了在整体系统仍处于非活性相时找到局部处于活性相的稀有区域的概率。具体而言，如果关联随距离的幂次衰减，稀有区域概率是稀有区域大小的拉伸指数函数，而不是像无关联无序情况那样是简单指数函数。结果，格里菲斯奇点增强并呈现非幂律形式。临界点本身是无限随机类型，但临界指数值与无关联情况不同。我们报告了大规模蒙特卡罗模拟，验证并阐明了我们的理论。我们还讨论了向更高维度的推广以及在其他系统中的应用，如随机横场伊辛模型、巡游磁体和超导体 - 金属转变。
