Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants
<p dir="ltr">Without Borel or Padé techniques, we show that for a divergent series with n! large-order growth factor, the set of hypergeometric series <sub>p</sub>F<sub>p</sub> -2 represents suitable approximants. The divergent<sub>p</sub>F<sub&...
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2020
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| author | Abouzeid M. Shalaby (16810695) |
| author_facet | Abouzeid M. Shalaby (16810695) |
| author_role | author |
| dc.creator.none.fl_str_mv | Abouzeid M. Shalaby (16810695) |
| dc.date.none.fl_str_mv | 2020-12-01T00:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.rinp.2020.103376 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Weak-coupling_strong-coupling_and_large-order_parametrization_of_the_hypergeometric-Meijer_approximants/24270283 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Numerical and computational mathematics Physical sciences Particle and high energy physics Non-Hermitian models PT -symmetry Resummation techniques Hypergeometric resummation |
| dc.title.none.fl_str_mv | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">Without Borel or Padé techniques, we show that for a divergent series with n! large-order growth factor, the set of hypergeometric series <sub>p</sub>F<sub>p</sub> -2 represents suitable approximants. The divergent<sub>p</sub>F<sub>p</sub>-2 series are then resummed via their representation in terms of the Meijer-G function. The choice of <sub>p</sub>F<sub>p</sub>-2 accelerates the convergence even with only weak-coupling information as input. For more acceleration of the convergence, we employ the strong-coupling and large-order information. We obtained a new constraint that relates the difference between the sum of the numerator and the sum of denominator parameters in the hypergeometric approximant to one of the large-order parameters. To test the validity of that constraint, we employed it to obtain the exact partition function of the zero-dimensional Ø<sup>4</sup> scalar field theory. The algorithm is also applied for the resummation of the ground state energies of Ø<sup>4</sup><sub>0+1</sub> and<sup>i</sup><sup>Ø</sup><sup>3</sup><sub>0+1</sub> scalar field theories. We get accurate results for the whole coupling space and the precision is improved systematically in using higher orders. Precise results for the critical exponents of the O(4)-symmetric field model in three dimensions have been obtained from resummation of the recent six-loops order of the corresponding perturbation series. The recent seven-loops order for the ß-function of the Ø<sup>4</sup><sub>3+1</sub> field theory has been resummed which shows non-existence of fixed points. The first resummation result of the seven-loop series representing the fractal dimension of the two-dimensional self-avoiding polymer is presented here where we get a very accurate value of d<sub>f</sub>=1.3307 compared to its exact value (4/3≈1.3333).</p><h2>Other Information</h2><p dir="ltr">Published in: Results in Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.rinp.2020.103376" target="_blank">https://dx.doi.org/10.1016/j.rinp.2020.103376</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_dfbb010c5be28659a69634a8fde5da78 |
| identifier_str_mv | 10.1016/j.rinp.2020.103376 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24270283 |
| publishDate | 2020 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximantsAbouzeid M. Shalaby (16810695)Mathematical sciencesNumerical and computational mathematicsPhysical sciencesParticle and high energy physicsNon-Hermitian modelsPT -symmetryResummation techniquesHypergeometric resummation<p dir="ltr">Without Borel or Padé techniques, we show that for a divergent series with n! large-order growth factor, the set of hypergeometric series <sub>p</sub>F<sub>p</sub> -2 represents suitable approximants. The divergent<sub>p</sub>F<sub>p</sub>-2 series are then resummed via their representation in terms of the Meijer-G function. The choice of <sub>p</sub>F<sub>p</sub>-2 accelerates the convergence even with only weak-coupling information as input. For more acceleration of the convergence, we employ the strong-coupling and large-order information. We obtained a new constraint that relates the difference between the sum of the numerator and the sum of denominator parameters in the hypergeometric approximant to one of the large-order parameters. To test the validity of that constraint, we employed it to obtain the exact partition function of the zero-dimensional Ø<sup>4</sup> scalar field theory. The algorithm is also applied for the resummation of the ground state energies of Ø<sup>4</sup><sub>0+1</sub> and<sup>i</sup><sup>Ø</sup><sup>3</sup><sub>0+1</sub> scalar field theories. We get accurate results for the whole coupling space and the precision is improved systematically in using higher orders. Precise results for the critical exponents of the O(4)-symmetric field model in three dimensions have been obtained from resummation of the recent six-loops order of the corresponding perturbation series. The recent seven-loops order for the ß-function of the Ø<sup>4</sup><sub>3+1</sub> field theory has been resummed which shows non-existence of fixed points. The first resummation result of the seven-loop series representing the fractal dimension of the two-dimensional self-avoiding polymer is presented here where we get a very accurate value of d<sub>f</sub>=1.3307 compared to its exact value (4/3≈1.3333).</p><h2>Other Information</h2><p dir="ltr">Published in: Results in Physics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.rinp.2020.103376" target="_blank">https://dx.doi.org/10.1016/j.rinp.2020.103376</a></p>2020-12-01T00:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.rinp.2020.103376https://figshare.com/articles/journal_contribution/Weak-coupling_strong-coupling_and_large-order_parametrization_of_the_hypergeometric-Meijer_approximants/24270283CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/242702832020-12-01T00:00:00Z |
| spellingShingle | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants Abouzeid M. Shalaby (16810695) Mathematical sciences Numerical and computational mathematics Physical sciences Particle and high energy physics Non-Hermitian models PT -symmetry Resummation techniques Hypergeometric resummation |
| status_str | publishedVersion |
| title | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| title_full | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| title_fullStr | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| title_full_unstemmed | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| title_short | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| title_sort | Weak-coupling, strong-coupling and large-order parametrization of the hypergeometric-Meijer approximants |
| topic | Mathematical sciences Numerical and computational mathematics Physical sciences Particle and high energy physics Non-Hermitian models PT -symmetry Resummation techniques Hypergeometric resummation |