# Calculation of critical exponents by self-similar factor approximants

@article{Yukalov2007CalculationOC, title={Calculation of critical exponents by self-similar factor approximants}, author={Vyacheslav I. Yukalov and E. P. Yukalova}, journal={The European Physical Journal B}, year={2007}, volume={55}, pages={93-99} }

Abstract.The method of self-similar factor approximants is applied to calculating
the critical exponents of the O(N)-symmetric ϕ4 theory and of the
Ising glass. It is demonstrated that this method, being much simpler than
other known techniques of series summation in calculating the critical
exponents, at the same time, yields the results that are in very good
agreement with those of other rather complicated numerical methods. The
principal advantage of the method of self-similar factor…

## 19 Citations

Calculating critical temperature and critical exponents by self-similar approximants

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Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and…

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The problem is analysed for extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar…

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The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are…

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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 method is suggested for calculating the critical temperature in multicomponent field theory with weak interactions. The method is based on self-similar approximation theory allowing for the…

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Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers…

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

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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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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…

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