Real space renormalization

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. 

In this chapter, we will focus on the entanglement behavior in QPT for the two-dimensional array of quantum dots, which provide a suitable arena for implementation of quantum computation [88, 89, 103]. For this purpose, the real-space renormalization group technique [91] will be utilized and developed for the finite-size analysis of entanglement. The model that we will be using is the Hubbard model [83],... 

Real-Space Renormalization, Topics in Current Physics (T. W. Burkhardt and J. M. J. van Leeuwen, eds.. Springer-Verlag, New York 1982. 

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. 

J.-P. MalrieuandN. Guihdry, Phys. Rev. B 63,5110,2001. These authors formulate a renormalization-group procedure where the renormalized Hamiltonian is defined as a Bloch effective Hamiltonian. This procedure is based on the real-space renormalization-group (RSRG) method (a) K. G. Wilson, Rev. Mod. Phys. 47, 773, 1975. (b) S.R. White and R.M. Noack, Phys. Rev. Lett. 68, 3487, 1992. 

Figure 32. Herringbone order parameter for the anisotropic-planar-rotor model (2.5) as a function of the reduced temperature T = TIK. Circles Monte Carlo results [244]. Dotted line mean-field approximation [62, 141]. Solid line triangular cluster-variational method [62]. Arrow first-order transition temperature obtained from a real-space renormalization group treatment of a planar quadrupolar six-state model [345]. (Adapted from Fig. 2 of Ref. 345.)...

Useful information can be obtained from models amenable to exact analysis even if they look artificial. Real space renormalization group approach can be handled in an exact fashion for a class of tailor-made lattices called hierarchical lattice. Such lattices are constructed in a recursive fashion as shown in Fig. 1. The problem of a directed polymer in a random medium on hierarchical lattices has been considered in Ref. [44,45]. Here we consider the RANI problem on hierarchical lattices. As already noted, the effective... 

The pure problem can be solved easily by a Real space renormalization approach where one needs only the renormalization of the Boltzmann factor y = exp(u/T). Let yniZn, and En be the renormalized weight, partition function and energy at the nth generation. By decimating the diamonds the recursion relations are given by... 

The set-up of the paper is as follows. In the following section we present the field-theoretical description of the polymer model, introduce different types of structural disorder into this model and present an introduction to real space renormalization. Section 3 reviews different treatments of these systems by field theoretical and real space RG approaches to analyze the scaling properties and to estimate the critical exponents. 

We now briefly indicate how the real-space renormalization group technique of the previous section can be extended to other fractals. 

Ag state was further investigated by Tavan and Schulten (1987). A real-space renormalization group calculation on the Hubbard-PeierIs model for chains of up... 

The EA model contains the two essential ingredients for a spin glass - disorder and competition as discussed above - but it is a crude approximation to real spin glasses. Therefore at the beginning we have to discuss how well this model reproduces spin-glass properties. Up to now there is no analytic solution available for the short-range EA model. Even modern methods like real space renormalization yield inconclusive results (Kinzel and Fischer 1978, Tatsumi 1978). Hence numerical methods like the Monte Carlo simulation have been applied to answer this question the results of which will be briefly summarized now. Then the mean-field analysis of the EA model will be discussed, and finally the question... 

Equation (94) was expected to apply in the case of not very different conductivities of components mor ver, it was derived assuming (p = 0.3 which differs significantly from the best theoretical estimates (cf. Table 1). In this respect, much more promising seems to be the approach based on the real space renormalization group (RSRG) theory [63] which provides for reasonable... 

Shah N, Ottino JM (1986) Effective transport properties of disordered, multi-phase composites. Application of real-space renormalization group theory. Chem Eng Sd 41 283-296... 

These nanostructures are described using a single-band tight-binding Hamiltonian and their electronic conductance and density of states are calculated within the Green s function formalism based on real-space renormalization techniques (Rosales et al. 2008). 

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