论文标题
分支以远距离排斥的分支歼灭随机步行：对数缩放，重入相变和交叉行为
Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors
论文作者
论文摘要
我们研究了具有远距离排斥的一维分支消灭随机行走中的吸收相变。排斥的实现是跳出偏见的方式，使粒子更有可能脱离其最接近的粒子。 The bias strength due to long-range interaction has the form $\varepsilon x^{-σ}$, where $x$ is the distance from a particle to its closest particle, $0\le σ\le 1$, and the sign of $\varepsilon$ determines whether the interaction is repulsive (positive $\varepsilon$) or attractive (negative $\varepsilon$).没有颗粒的状态是吸收状态。我们找到一个阈值$ \ varepsilon_s $，因此，如果$ \ varepsilon <\ varepsilon_s $，吸收状态对于小型分支速率$ q $动态稳定。阈值明显不同，具体取决于后代的数字$ \ ell $的均等。当$ \ varepsilon> \ varepsilon_s $时，具有奇数$ \ ell $的系统可以显示出从非零稳态密度到吸收阶段的活性阶段的重新进入相变，然后回到活动阶段。另一方面，如果$ \ varepsilon> \ varepsilon_s $，则具有$ \ ell $的系统在非零$ q $中处于活动阶段。尽管如此，对于$ \ ell = 2 $，仍有重入的相转换。但是，与奇数$ \ ell $的情况不同，只能以$σ= 1 $和$ 0 <\ varepsilon <\ varepsilon_s $而发生rectrant相变。当交互吸引人时（负$ \ varepsilon $）时，我们还研究了$ \ ell = 2 $的交叉行为，以找到交叉指数$ ϕ = 1.123（13）$ for $σ= 0 $。
We study absorbing phase transitions in the one-dimensional branching annihilating random walk with long-range repulsion. The repulsion is implemented as hopping bias in such a way that a particle is more likely to hop away from its closest particle. The bias strength due to long-range interaction has the form $\varepsilon x^{-σ}$, where $x$ is the distance from a particle to its closest particle, $0\le σ\le 1$, and the sign of $\varepsilon$ determines whether the interaction is repulsive (positive $\varepsilon$) or attractive (negative $\varepsilon$). A state without particles is the absorbing state. We find a threshold $\varepsilon_s$ such that the absorbing state is dynamically stable for small branching rate $q$ if $\varepsilon < \varepsilon_s$. The threshold differs significantly, depending on parity of the number $\ell$ of offspring. When $\varepsilon>\varepsilon_s$, the system with odd $\ell$ can exhibit reentrant phase transitions from the active phase with nonzero steady-state density to the absorbing phase, and back to the active phase. On the other hand, the system with even $\ell$ is in the active phase for nonzero $q$ if $\varepsilon>\varepsilon_s$. Still, there are reentrant phase transitions for $\ell=2$. Unlike the case of odd $\ell$, however, the reentrant phase transitions can occur only for $σ=1$ and $0<\varepsilon < \varepsilon_s$. We also study the crossover behavior for $\ell = 2$ when the interaction is attractive (negative $\varepsilon$), to find the crossover exponent $ϕ=1.123(13)$ for $σ=0$.
