We consider the random-bond Potts model in the large-$Q$ limit and calculate the excess entropy, $S_Γ$, of a contour, $Γ$, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by $Γ$. In two dimensions $S_Γ$ is proportional to the length of $Γ$, to which - at the critical point - there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: $\lim_{Q \to \infty}c(Q)/\ln Q =0.74(2)$, close to previous estimates calculated at finite values of $Q$.
Star-graph expansions for bond-diluted Potts models
利用星型展开技术，推导了超立方晶格上无规键$q$态Potts模型的自由能和磁化率的高温级数展开式.这种方法能够精确计算任意非关联耦合分布的淬火无序平均值。此外，我们可以保持无序强度$p$以及维数$d$作为符号参数。通过将几种级数分析技术应用于新的级数展开式，可以扫描$(p,d)$参数空间的大区域以寻找$q$的任何值。对于键稀释的4-状态Potts模型在三维空间中，这表现出一个相当强的一级相变在未稀释的情况下，我们提出的结果作为$p$的函数的转变温度和有效的临界指数$γ$的磁化率序列的分析，以达到18阶。与最近的蒙特卡罗数据（Chatelain { \em et al.}，E64，036120（2001））示出了在有限无序强度下软化到二级转变的信号。
We consider the two-dimensional random bond $q$-state Potts model within the recently introduced exact framework of scale invariant scattering, exhibit the line of stable fixed points induced by disorder for arbitrarily large values of $q$, and examine the renormalization group pattern for $q>4$, when the transition of the pure model is first order.
To address some physical properties of percolating systems it can be useful to know the degree distributions in finite clusters along with their size distribution. Here we show that to achieve this aim for classical bond percolation one can use the $q \to 1$ limit of suitably modified q-state Potts model. We consider a version of such model with the additional complex variables and show that its partition function gives generating function for the size and degree distribution in this limit. We derive this distribution analytically for bond percolation on Bethe lattice and complete graph. The p…
The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-or…
High-density (HD) percolation describes the percolation over specific $κ$ -clusters, which are the compact sets of sites each connected to $κ$ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exsists. Hence, the study of series of $κ$ -type percolations amounts to the description of structure of classical clusters for which $κ$ -clusters constitute $κ$ -cores nested one into another. Such data are needed for description of a number of physical, biological information and other p…
Several amorphous silicon structures were generated using a classical molecular dynamics (MD) protocol of melting and quenching with different quenching rates. An analysis of the calculated electronic properties of these structures revealed that the midgap state density of a-Si which is of interest for solar cell and thin film transistor applications can be correlated to bond angle standard deviation. We also found that this parameter can strongly determine the excess energy of a-Si, which is an important criteria in theoretically generating realistic atomic structures of a-Si.
