Phase diagram和对湮灭模型的临界行为
Phase diagram and critical behavior of the pair annihilation model
摘要：
利用对近似（PA）和蒙特卡罗模拟，研究了一维、二维和三维带扩散的对湮灭模型（PAM）的临界行为。主要的兴趣是临界产生率，λ_c，对扩散概率D的依赖性，特别是，是否生存可能在任意小的产生率，足够快的扩散。虽然PA预测在任何空间维度d \geq 1中，在某个扩散概率D* < 1时λ_c> 0，但Katori和Konno [Physica A { \bf 186}，578（1992）]严格地表明，对于d \leq 2，对于任何D<1，都有λ_c > 0。我们的模拟结果与这个定理是一致的。在二维中，消光区随着D接近1而变窄，遵循λ_c \propto \exp [- \rm{const.} /（1-D）^γ]，其中γ = 1.41（2）。在三维空间中，我们发现D* = 0.333（3）。模拟结果证实了PAM属于定向渗流普适类。
英文摘要：
We study the critical behavior of the pair annihilation model (PAM) with diffusion in one, two and three dimensions, using the pair approximation (PA) and Monte Carlo simulation. Of principal interest is the dependence of the critical creation rate, lambda_c, on the diffusion probability D, in particular, whether survival is possible at arbitrarily small creation rates, for sufficiently rapid diffusion. Whilst the PA predicts that in any spatial dimension d \geq 1, lambda_c -> 0 at some diffusion probability D* < 1, Katori and Konno [Physica A {\bf 186}, 578 (1992)] showed rigorously that for d \leq 2, one has lambda_c > 0 for any D<1. Our simulation results are consistent with this theorem. In two dimensions, the extinction region becomes narrow as D approaches unity, following lambda_c \propto \exp[- \rm{const.}/(1-D)^γ], with gamma = 1.41(2). In three dimensions we find D* = 0.333(3). The simulation results confirm that the PAM belongs to the directed percolation universality class.
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