Albuquerque S S, de Moura F A B F, Lyra M L, de Souza A J F
Departamento de Física, Universidade Federal de Alagoas, Maceió-AL, 57072-970, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016116. doi: 10.1103/PhysRevE.72.016116. Epub 2005 Jul 18.
Relying on the fractal character of the largest clusters at criticality, we employ a finite-size scaling analysis to obtain an accurate phase-diagram of the percolation transition in chains with bond concentration decaying as a power-law on the form 1/ r(1+sigma) . For the particular case of sigma=1, no percolation transition is observed to occur at a finite dilution, in contrast with the finite temperature Kosterlitz-Thouless transition exhibited in Ising and Potts chains with inverse square-law couplings. The fractal dimension of the critical percolation cluster is found to follow distinct dependencies on the decay exponent being numerically fitted by d(f) =0.35+4sigma/5 for 0<sigma<1/2 and d(f) = (1+sigma) /2 for 1/2<sigma<1 . We also compute average mass ratios of the two largest clusters at criticality.
基于临界状态下最大团簇的分形特征，我们采用有限尺寸标度分析来获得键浓度以幂律形式(1/r^{(1 + \sigma)})衰减的链中渗流转变的精确相图。对于(\sigma = 1)的特殊情况，与具有平方反比耦合的伊辛链和Potts链中表现出的有限温度Kosterlitz - Thouless转变不同，未观察到在有限稀释时发生渗流转变。发现临界渗流团簇的分形维数对衰减指数呈现出不同的依赖性，在数值上对于(0 < \sigma < 1/2)拟合为(d(f) = 0.35 + 4\sigma/5)，对于(1/2 < \sigma < 1)拟合为(d(f) = (1 + \sigma)/2)。我们还计算了临界状态下两个最大团簇的平均质量比。
