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This article is cited in 8 scientific papers (total in 8 papers)
Critical exponents and the pseudo-$\varepsilon$-expansion
M. A. Nikitinaab, A. I. Sokolova a St. Petersburg State University,
Fock Research Institute of Physics, St. Petersburg, Russia
b St. Petersburg National Research University for Information
Technologies, Mechanics, and Optics, St. Petersburg, Russia
Abstract:
We present the pseudo-$\varepsilon$-expansions ($\tau$-series) for the critical exponents of a $\lambda\phi^4$-type three-dimensional $O(n)$-symmetric model obtained on the basis of six-loop renormalization-group expansions. We present numerical results in the physically interesting cases $n=1$, $n=2$, $n=3$, and $n=0$ and also for $4\le n\le32$ to clarify the general properties of the obtained series. The pseudo-$\varepsilon$-expansions or the exponents $\gamma$ and $\alpha$ have coefficients that are small in absolute value and decrease rapidly, and direct summation of the $\tau$-series therefore yields quite acceptable numerical estimates, while applying the Padé approximants allows obtaining high-precision results. In contrast, the coefficients of the pseudo-$\varepsilon$-expansion of the scaling correction exponent $\omega$ do not exhibit any tendency to decrease at physical values of $n$. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Padé approximants in this case. The pseudo-$\varepsilon$-expansion technique can therefore be regarded as a distinctive resummation method converting divergent renormalization-group series into expansions that are computationally convenient.
Keywords:
three-dimensional $O(n)$-symmetric model, critical exponent, pseudo-$\varepsilon$-expansion, Padé approximant, numerical result.
Received: 14.05.2015
Citation:
M. A. Nikitina, A. I. Sokolov, “Critical exponents and the pseudo-$\varepsilon$-expansion”, TMF, 186:2 (2016), 230–242; Theoret. and Math. Phys., 186:2 (2016), 192–204
Linking options:
https://www.mathnet.ru/eng/tmf8966https://doi.org/10.4213/tmf8966 https://www.mathnet.ru/eng/tmf/v186/i2/p230
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Abstract page: | 331 | Full-text PDF : | 132 | References: | 36 | First page: | 17 |
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