一类精确求解的直线上主动吸收态跃迁的辅助跳跃模型
A class of exactly solved assisted hopping models of active-absorbing state transitions on a line
摘要：
我们构造了一类一维辅助跳跃模型，其中粒子只有在不位于长度大于$n+1$的空区间内时才能移动。我们确定的确切的稳态映射到气体的缺陷，只有现场相互作用。我们表明，该系统经历了相变作为密度$ρ$的粒子的函数，从低密度相与所有粒子不动的$ρ\le ρ_c = \frac{1}{n+1}$，一个活跃的状态为$ρ> ρ_c$。对于在$ρ_c$附近的$ρ$，活动稳态中可移动粒子的平均分数随$(ρ- ρ_c)^β$变化。我们表明，对于模型与范围$n$，指数$β=n$，因此可以任意大。
英文摘要：
We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than $n+1$. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density $ρ$ of particles, from a low-density phase with all particles immobile for $ρ\le ρ_c = \frac{1}{n+1}$, to an active state for $ρ> ρ_c$. The mean fraction of movable particles in the active steady state varies as $(ρ- ρ_c)^β$, for $ρ$ near $ρ_c$. We show that for the model with range $n$, the exponent $β=n$, and thus can be made arbitrarily large.
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