论文标题
分支在一个维
Branching annihilating random walks with long-range attraction in one dimension
论文作者
论文摘要
我们介绍并数字研究具有远距离吸引力（Bawl）的分支歼灭随机步行。远距离吸引力使跳跃的偏向方式使粒子沿着向最近粒子的方向跳跃的过渡速率比朝向方向跳跃更大。尽管如此，与Lévy飞行不同，粒子只能跳到其最近的邻居站点之一。偏差的强度采用非阴性$σ$的$ x^{ - σ} $的形式，其中$ x $是距离粒子到hop的最近粒子的距离。通过广泛的蒙特卡洛模拟，我们表明，关键的衰减指数$δ$连续变化，$σ$最高$σ= 1 $，$δ$与定向的ISING（DI）通用类的关键衰减指数相同，$σ\ ge 1 $。在研究吸收阶段密度的行为时，我们认为$σ= 1 $的确是将DI和非DI临界行为分开的阈值。我们还通过Monte Carlo模拟显示，与对称跳跃的分支偏置表现出与Bawl相同的临界行为。
We introduce and numerically study the branching annihilating random walks with long-range attraction (BAWL). The long-range attraction makes hopping biased in such a manner that particle's hopping along the direction to the nearest particle has larger transition rate than hopping against the direction. Still, unlike the Lévy flight, a particle only hops to one of its nearest-neighbor sites. The strength of bias takes the form $x^{-σ}$ with non-negative $σ$, where $x$ is the distance to the nearest particle from a particle to hop. By extensive Monte Carlo simulations, we show that the critical decay exponent $δ$ varies continuously with $σ$ up to $σ=1$ and $δ$ is the same as the critical decay exponent of the directed Ising (DI) universality class for $σ\ge 1$. Investigating the behavior of the density in the absorbing phase, we argue that $σ=1$ is indeed the threshold that separates the DI and non-DI critical behavior. We also show by Monte Carlo simulations that branching bias with symmetric hopping exhibits the same critical behavior as the BAWL.
