Lübeck S, Janssen H-K
Institut für Theoretische Physik, Universität-Duisburg-Essen, D-47048 Duisburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016119. doi: 10.1103/PhysRevE.72.016119. Epub 2005 Jul 19.
We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the nonequilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.
我们通过解析和数值方法研究了平均场区域内有向渗流非平衡相变附近稳态下的有限尺寸标度行为，即高于上临界维度的情况。与平衡态类似，通常的有限尺寸标度在上临界维度以下是有效的，而在其之上则失效。通过对相关路径积分进行动量分析，我们推导出了序参量及其高阶矩的修正有限尺寸标度形式。相应高维晶格模型的数值模拟证实了这些结果。
