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摘要翻译：
近年来，对平衡体系中有限尺度标度的理解取得了相当大的进展。在这里，我们研究了在有向渗流(DP)的情况下，非平衡体系中的有限尺度标度，有向渗流已经成为非平衡相变到吸收态的范例，在上临界维数以上，在上临界维数以下。在有限边长L的D维超立方体上，在体临界点附近有周期边界条件，考虑均匀恒定外源作用下DP的定常态，分析和数值研究了DP的有限尺度标度行为。特别地，我们用重整化场理论研究了序参量及其高阶矩。我们导出了单环计算中矩的有限尺寸标度形式。此外，我们引入并计算了一个序参量矩的比值，它在分析吸收非平衡过程中的有限尺度标度时起着类似于平衡系统中著名的Binder累积量的作用，特别是提供了DP普适类的一个新的特征。为了补充我们的分析工作，我们进行了蒙特卡罗模拟，证实了我们的分析结果。
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英文标题：
《Finite-size scaling of directed percolation in the steady state》
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作者：
Hans-Karl Janssen, Sven Lubeck, Olaf Stenull
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.
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PDF链接：
https://arxiv.org/pdf/705.132
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