Odor G, Marques M C, Santos M A
Research Institute for Technical Physics and Materials Science, P. O. Box 49, H-1525 Budapest, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 2):056113. doi: 10.1103/PhysRevE.65.056113. Epub 2002 May 16.
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths (D). We found that N>2 cluster mean-field approximations must be considered to get consistent singular behavior. The N=3,4 approximations result in a continuous phase transition belonging to a single universality class along the D subset (0,1) phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting the bosonic field theoretical prediction that the upper critical dimension in this model is d(c)=2. The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D=0 end point of the transition line we found directed percolation criticality.
我们研究了二维中不同粒子扩散强度（D）下二元扩散过程的相变行为。我们发现，必须考虑N>2团簇平均场近似才能得到一致的奇异行为。N = 3、4近似导致沿着D子集（0,1）相变线属于单一普适类的连续相变。粒子密度的大规模模拟证实了具有对数修正的平均场标度行为。这被解释为支持玻色场理论预测的数值证据，即该模型中的上临界维度为d(c)=2。对密度以类似方式标度，但对比序参量有一个额外的对数因子。在相变线的D = 0端点，我们发现了定向渗流临界性。
