Renormalization group applications

In good solvents, the mean force is of the repulsive type when the two polymer segments come to a close distance and the excluded volume is positive this tends to swell the polymer coil which deviates from the ideal chain behavior described previously by Eq. (1). Once the excluded volume effect is introduced into the model of a real polymer chain, an exact calculation becomes impossible and various schemes of simplification have been proposed. The excluded volume effect, first discussed by Kuhn [25], was calculated by Flory [24] and further refined by many different authors over the years [27]. The rigorous treatment, however, was only recently achieved, with the application of renormalization group theory. The renormalization group techniques have been developed to solve many-body problems in physics and chemistry. De Gennes was the first to point out that the same approach could be used to calculate the MW dependence of global properties... 

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. 

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. 

Chan, G.K.L., Van Voorhis, T. Density-matrix renormalization-group algorithms with nonortho-gonal orbitals and non-Hermitian operators, and applications to polyenes. J. Chem. Phys. 2005, 122(20), 204101. 

Two methods appear to be very powerful for the study of critical phenomena field theory as a description of many-body systems, and cell methods grouping together sets of neighboring sites and describing them by an effective Hamiltonian. Both methods are based on the old idea that the relevant scale of critical phenomena is much larger than the interatomic distance and this leads to the notion of scale invariance and to the statistical applications of the renormalization group technique.93... 

I am now at the end of my series of flashes on the Solvay Conferences in Physics. I hope that, in spite of its shortness and incompleteness, it may help in stimulating two kinds of considerations. Those of the first kind regard the extraordinary develoment undergone during the last 70 years by our views on the physical world, many parts of which in present days appear to be dominated by a few general concepts, such as those of exact and approximate symmetry, and to be treatable by mathematical procedures such as the application of the renormalization group. The other kind of considerations concerns the role that the Solvay Conferences in Physics have played in the development of physics during the last 70 years, and the unique value they will maintain, even in the future, as sources of information for the historians of science. 

Finally, for completeness in Appendix A 7.1 we consider the formal relation of the continuous chain model to a field theoretic Hamiltonian, used to describe critical phenomena in ferrornagnets. It was this relation discovered by de Genries [dG72] and extended by Des Cloizeaux [Clo75, which initiated the application of the renormalization group to polymer solutions and led to the embedding into the larger realm of critical phenomena. 

D. Shalloway, Application of the renormalization group to deterministic global minimization of molecular conformation energy functions. Journal of Global Optimization 2 (1992), 281. 

Since the Renormalization Group approach is strictly applicable only for very long polymers, we take the limit of Equation 17 as N becomes very large to obtain Equation 18. 

Unfortunately, theoretical understanding of polyelectrolytes is less developed than the understanding of the properties of neutral polymers. Some reasons are that the presence of long-range interactions renders the application of renormalization group techniques and scaling ideas much more difficult than in the neutral case. The reason is that many new length scales... 

The role of interchain coupling. Renormalization group methods earlier applied to ID systems have been extended to treat two or more interacting chains, with applications to the 4k problem. Extensions have been given of the Bak-Emory theory of the 38°, 49° and 54°K transitions in TTF-TCNQ in which Coulomb interactions between CDW s on different chains play an important role. Another question is how much 3D effects reduce fluctuations above Tc expected for ID systems. 

The Density Matrix Renormalization Group Method Application to the Low-lying Electronic States in Conjugated Polymers... 

Saveiyev, A., and Papoian, G. A. (2009a). Molecular renormalization group coarse-graining of electrol5d e solutions Application to aqueous NaCl and KCi, The Journal of Physical Chemistry B113, 22, pp. 7785-7793. 

Legeza, O., Noack, R., Solyom, ]. and Tincani, L. (2008) Applications of quantum information in the density-matrix renormalization group, in Computational Many-Particle Physics, vol. 739 (eds H. Fehske, R. Schneider and A. Weisse), Springer, Berlin/Heidelberg. 

Renormalization group (RG) techniques are applicable to SAWs on percolation and have... 

The density matrix renormalization group (DMRG) method is an efficient and accurate Hilbert space truncation procedure (White 1992 1993) that can be used to solve quantum mechanical models on very large systems. It is particularly suited for one-dimensional quantum lattice models, such as the 7r-electron models discussed in this book. This appendix contains a brief review of the DMRG method relevant for these models. A full discussion of the method and its various applications may be found in (Peschel et al. 1999), (Dukelsky and Pittel 2004), or (Schollwock 2005). 

O. Legeza, R. M. Noack, J. Sdlyom, L. fin-cani. Applications of Quantum Information in the Density-Matrix Renormalization Group. In H. Fehske, R. Schneider,... 

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