Suppr超能文献

二维布鲁姆-卡佩尔模型中空位间的渗流。

Percolation between vacancies in the two-dimensional Blume-Capel model.

作者信息

Deng Youjin, Guo Wenan, Blöte Henk W J

机构信息

Laboratory for Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016101. doi: 10.1103/PhysRevE.72.016101. Epub 2005 Jul 1.

Abstract

Using suitable Monte Carlo methods and finite-size scaling, we investigate the Blume-Capel model on the square lattice. We construct percolation clusters by placing nearest-neighbor bonds between vacancies with a variable bond probability p(b) . At the tricritical point, we locate the percolation threshold of these vacancy clusters at p(bc) =0.706 33 (6) . At this point, we determine the fractal dimension of the vacancy clusters as Xf =0.1308 (5) approximately equal to 21/160, and the exponent governing the renormalization flow in the p(b) direction as y(p) =0.426 (2) approximately equal to 17/40 . For bond probability p(b) > p(bc) , the vacancy clusters maintain strong critical correlations; the fractal dimension is Xf =0.0750 (2) approximately equal to 3/40 and the leading correction exponent is y(p) =-0.45 (2) approximately equal to -19/40 . The above values fit well in the Kac table for the tricritical Ising model. These vacancy clusters have much analogy with those consisting of Ising spins of the same sign, although the associated quantities rho and magnetization m are energylike and magnetic quantities, respectively. However, along the critical line of the Blume-Capel model, the vacancies are more or less uniformly distributed over the whole lattice. In this case, no critical percolation correlations are observed in the vacancy clusters, at least in the physical region p(b) < or = 1 .

摘要

我们使用合适的蒙特卡罗方法和有限尺寸标度,研究了正方晶格上的布卢姆 - 卡佩尔模型。我们通过以可变键概率(p(b))在空位之间放置最近邻键来构建渗流团簇。在三临界点,我们确定这些空位团簇的渗流阈值为(p(bc)=0.70633(6))。此时,我们确定空位团簇的分形维数为(Xf = 0.1308(5)),约等于(21/160),以及控制(p(b))方向重整化流的指数为(y(p)=0.426(2)),约等于(17/40)。对于键概率(p(b)>p(bc)),空位团簇保持强临界相关性;分形维数为(Xf = 0.0750(2)),约等于(3/40),主导修正指数为(y(p)= -0.45(2)),约等于(-19/40)。上述值与三临界伊辛模型的卡茨表拟合良好。这些空位团簇与由相同符号的伊辛自旋组成的团簇有很多相似之处,尽管相关量(\rho)和磁化强度(m)分别是类能量量和磁量。然而,沿着布卢姆 - 卡佩尔模型的临界线,空位或多或少均匀地分布在整个晶格上。在这种情况下,至少在物理区域(p(b)\leq1)中,空位团簇中未观察到临界渗流相关性。

文献AI研究员

20分钟写一篇综述,助力文献阅读效率提升50倍。

立即体验

用中文搜PubMed

大模型驱动的PubMed中文搜索引擎

马上搜索

文档翻译

学术文献翻译模型,支持多种主流文档格式。

立即体验