Hooyberghs J, Carlon E, Vanderzande C
Departement WNI, Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036124. doi: 10.1103/PhysRevE.64.036124. Epub 2001 Aug 30.
We investigate the critical properties of a one-dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with n</=4 by means of the nonhermitian density-matrix renormalization group. For n=1 and n=2 we find that the model is, respectively, in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit, the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results, we conjecture that the model is in the same universality class for all n>/=3 with exponents z=nu( ||)/nu( perpendicular)=2, nu( perpendicular)=1, and beta=1. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one (Z2), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.
我们研究了一个具有(n)个（置换对称）吸收态的一维随机晶格模型的临界性质。我们通过非厄米密度矩阵重整化群分析了(n\leq4)的情况。对于(n = 1)和(n = 2)，我们发现该模型分别处于有向渗流和奇偶守恒普适类中，这与先前的研究一致。对于(n = 3)和(n = 4)，该模型在整个参数空间中处于活跃相，临界点移至一个无限反应速率的极限处。我们表明，在此极限下，该模型的动力学可以映射到零温度(n)态Potts模型的动力学上。基于我们的数值和分析结果，我们推测对于所有(n\geq3)，该模型处于相同的普适类中，其指数为(z=\nu_{||}/\nu_{\perp}=2)，(\nu_{\perp}=1)，以及(\beta = 1)。这些指数与多物种（玻色子）分支湮灭随机游走的指数一致。对于(n = 3)，我们还表明，当将对称性破缺到较低对称性（(Z_2)）时，根据参数的选择，会得到一个处于有向渗流或奇偶守恒类中的转变。
