论文标题
配对接触过程的耦合两种模型与扩散
A coupled two-species model for the pair contact process with diffusion
论文作者
论文摘要
由二进制反应2 B-> 3 B，2 B-> 0定义的扩散（PCPD）的接触过程和扩散粒子扩散表现出一种不寻常的活性到吸收相变，其普遍性类别长期存在。多项研究表明，可能需要对粒子对自由度的明确描述才能正确捕获该系统有效的长期大规模行为。我们介绍了两个物种表示，其中单个颗粒B和对A根据随机反应B + B-> a，A-> A + B，A-> 0和A-> B + B耦合。平均值场分析表明，相位过渡是由两种物种之间的竞争和平衡驱动的。我们采用蒙特卡洛模拟来证明该模型捕获了相关的PCPD功能。在不活跃的阶段，一个颗粒迅速灭绝，使B物种进行纯对歼灭动力学。在临界时，A和B密度都具有与PCPD顺序参数相同的指数的衰减，并在临界维度2上方显示平均场缩放。在一个维度中，从种子模拟获得的B物种的临界指数与先前报道的指数值吻合。我们证明，PCPD中连续粒子对的缩放特性与耦合模型中的A物种相同。这两种物种图片解决了原始PCPD中种子模拟的概念困难，并且自然引入了多个长度和时间尺度，从而导致缩放的较大校正。从我们的模拟中提取的力矩比表明我们的模型显示与PCPD相同的时间交叉行为，这进一步证实了其与我们的耦合模型的完整动态对等。
The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies have indicated that an explicit account of particle pair degrees of freedom may be required to properly capture this system's effective long-time, large-scale behavior. We introduce a two-species representation in which single particles B and pairs A are coupled according to the stochastic reactions B + B -> A, A -> A + B, A -> 0, and A -> B + B. Mean-field analysis reveals that the phase transition is driven by competition and balance between both species. We employ Monte Carlo simulations to demonstrate that this model captures the pertinent PCPD features. In the inactive phase, A particles rapidly go extinct, leaving the B species to undergo pure pair annihilation kinetics. At criticality, both A and B densities decay with the same exponents as the PCPD order parameters, and display mean-field scaling above the critical dimension 2. In one dimension, the critical exponents for the B species obtained from seed simulations agree well with previously reported exponent values. We demonstrate that the scaling properties of consecutive particle pairs in the PCPD are identical with that of the A species in the coupled model. This two-species picture resolves the conceptual difficulty for seed simulations in the original PCPD and naturally introduces multiple length and time scales, which cause strong corrections to scaling. The extracted moment ratios from our simulations indicate that our model displays the same temporal crossover behavior as the PCPD, which further corroborates its full dynamical equivalence with our coupled model.
