Renormalization group methods

The scaling argument provides only the exponent but not the absolute numerical value for the constant. Therefore, for quantitative results, it should be completed by some more refined technique like the afore-mentioned renormalization group method [49],... 

In order to be useful in practice, the effective transport coefficients have to be determined for a porous medium of given morphology. For this purpose, a broad class of methods is available (for an overview, see [191]). A very straightforward approach is to assume a periodic structure of the porous medium and to compute numerically the flow, concentration or temperature field in a unit cell [117]. Two very general and powerful methods are the effective-medium approximation (EMA) and the position-space renormalization group method. 

As a second method to determine effective transport coefficients in porous media, the position-space renormalization group method will be briefly discussed. 

Although in principle a powerful and elegant method, the position-space renormalization group method yields very complex expressions for the renormalized... 

The lattice gas model of Bell et al. [33] neither gave any detailed mechanism of the orientational ordering nor separated the contributions of the headgroup and the acyl chain. Lavis et al. [34] discussed Ref. 33 critically and concluded that the sharp kink point in the isotherm at transition was an artifact of the mean field approximation used. An improved correspondence to experimental data was claimed by the use of the real-space renormalization group method [35]. The same authors returned to the problem [35] and concluded that in addition to the orientation of the molecules, chain melting had to be included in a model which could interpret the phase transitions. 

Our group has made extensive use of the RNG k-e model (Nijemeisland and Dixon, 2004), which is derived from the instantaneous Navier-Stokes equations using the Renormalization Group method (Yakhot and Orszag, 1986) as opposed to the standard k-e model, which is based on Reynolds averaging. The... 

Legeza, O., Solyom, J. Optimizing the density-matrix renormalization group method using quantum information entropy. Phys. Rev. B 2003, 68(19), 195116. 

Ramasesha, S., Pati, S.K., Krishnamurthy, H.R., Shuai, Z., Bredas, J.L. Low-lying electronic excitations and nonlinear optic properties of polymers via symmetrized density matrix renormalization group method. Synth. Met. 1997, 85(1-3), 1019. 

Fano, G., Ortolani, F., Ziosi, L. The density matrix renormalization group method Application to the PPP model of a cyclic polyene chain. J. Chem. Phys. 1998, 108(22), 9246. 

Zgid, D., Nooijen, M. On the spin and symmetry adaptation of the density matrix renormalization group method. J. Chem. Phys. 2008, 128, 014107. 

Kurashige, Y., Yanai, T. High-performance ab initio density matrix renormalization group method applicability to large-scale multireference problems for metal compounds. J. Chem. Phys. 2009, 130(23), 234114. 

An improved treatment is obtained by renormalization group methods, which lead to the absence of long-range order at any finite temperature [26]. However, interactions now become temperature dependent. A very simple illustration of the one-dimensional behavior is provided by the first-order renormalization calculation of gx and g2, which become... 

Renormalization group method can be used to determine the flow of renormalization for (g, gj, g 4) when these act as perturbations for the Luttinger liquid parameters (K, uf) as a function of energy. 

One-particle spectral properties of a Luttinger liquid. The absence of quasiparticles in a Luttinger liquid is also manifest in the one-particle spectral properties. As we have seen in the framework of the ID renormalization group method in the gapless case, there is a power-law decay of the one-particle spectral weight at the Fermi level. This power law behavior is also confirmed in the framework of the bosonization technique [146, 147], namely... 

In summary, by using a multistage real-space renormalization group method, we show that the finite-size scaling can be applied in Mott MIT. And the dynamic and correlation length critical exponents are found to be z = 0.91 and v = 1, respectively. At the transition point, the charge gap scales with size as Ag 1/L0-91. 

The result of the renormalization group method as applied to percolation problems consists of the following a physical state characterized, for instance, by the parameters To evolving via a set of equations Y forms a continuous sequence of new effective equations T(/), characterized by the new parameters... 

The finite temperature studies of Lennard-Jones lattice gas systems have been performed for the square [105,116], rectangular [106] and triangular [100,111,112] lattices using different approaches, including the simple mean-field theory, the renormalization group method, Monte Carlo simulation and Monte Carlo version of the coherent anomaly method. 

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