CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India.
Phys Rev E. 2017 Oct;96(4-1):042120. doi: 10.1103/PhysRevE.96.042120. Epub 2017 Oct 9.
Conserved lattice-gas models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents β=1=ν=η, whereas the same on a ladder belong to directed percolation (DP) universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder forces the APT to be in the DP class. To substantiate this we introduce a class of restricted conserved lattice-gas models on a multichain system (M×L square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains, in the thermodynamic limit L→∞, these models exhibit APT at ρ_{c}=1/2(1+1/M) with β=1. On the other hand, for even-chain systems transition occurs at ρ_{c}=1/2 with β=1,2 for M=2,4, respectively, and β=3 for M≥6. We illustrate this unusual critical behavior analytically using a transfer-matrix method.
一维的守恒格子气模型表现出具有简单整数指数β=1=ν=η的吸收态相变（APT），而 ladder 上的相同模型属于定向渗流（DP）的普遍性。我们推测，粒子转移中的额外随机性是一个相关的微扰，其在 ladder 上的存在迫使 APT 处于 DP 类。为了证实这一点，我们在多链系统（M×L 正方形晶格，在两个方向上具有周期性边界条件）上引入了一类受限的守恒格子气模型，其中只有一个空位邻居的粒子是活跃的，它们确定性地移动到相邻的空位。我们表明，对于奇数个链，在热力学极限 L→∞ 下，这些模型在 ρ_{c}=1/2(1+1/M) 处表现出 APT，β=1。另一方面，对于偶数链系统，当 M=2,4 时，过渡发生在 ρ_{c}=1/2 处，β=1,2，而当 M≥6 时，β=3。我们使用转移矩阵方法进行了分析，说明了这种不寻常的临界行为。
