# Interplay between Approximation Theory and Renormalization Group

@article{Yukalov2019InterplayBA, title={Interplay between Approximation Theory and Renormalization Group}, author={Vyacheslav I. Yukalov}, journal={Physics of Particles and Nuclei}, year={2019} }

The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory in powers of these parameters, and even when small parameters exist, the related perturbative series are strongly divergent. Second, such perturbative series in powers of these parameters are rather short, so that the standard resummation techniques either…

## 16 Citations

Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

- PhysicsInternational Journal of Modern Physics B
- 2020

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even…

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We handle divergent ϵ expansions in the different universality classes derived from modified Landau–Wilson Hamiltonian. Landau–Wilson Hamiltonian can cater for describing critical phenomena on a wide…

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The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to…

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Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Padé…

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A model of two coupled complex scalar fields is studied at finite temperature and under an external magnetic field. The results are obtained in the context of the nonperturbative method of the…

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Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review.

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We use continued functions to determine the universal critical exponents that describe the continuous phase transitions in different dimensions of space.

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- 2019

Optical lattices are considered loaded by atoms or molecules that can exhibit strong interactions between different lattice sites. The strength of these interactions can be sufficient for generating…

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- Mathematics, Physics
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We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pade approximants t...

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