Vojta Thomas, Farquhar Adam, Mast Jason
Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jan;79(1 Pt 1):011111. doi: 10.1103/PhysRevE.79.011111. Epub 2009 Jan 12.
We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte Carlo simulations for times up to 10;{10} and system sizes up to 8000x8000 sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because, according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.
我们通过大规模蒙特卡罗模拟研究了随机稀释晶格上二维接触过程中的非平衡相变，模拟时间长达(10^{10})，系统大小达到(8000×8000)个格点。我们的数据提供了强有力的证据，表明该相变由具有激活（指数）动力学标度的奇异无限随机性临界点控制。我们计算了相变的临界指数，发现它们是普适的，即与无序强度无关。清洁临界点和脏临界点之间的格里菲斯区域表现出幂律动力学标度，其指数连续变化。我们讨论了我们发现的普遍性，并将其与具有淬火无序的相变中稀有区域效应的更广泛理论联系起来。我们的结果不仅对于吸收态相变具有重要意义，因为根据强无序重整化群分析，我们的相变属于二维随机横向场伊辛模型的普适类。
