Six-loop renormalization group analysis of the model.
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| Title: | Six-loop renormalization group analysis of the model. |
|---|---|
| Authors: | Adzhemyan, L. Ts.1,2 (AUTHOR), Kompaniets, M. V.1,2 (AUTHOR) mkompan@gmail.com, Trenogin, A. V.1,2 (AUTHOR) |
| Source: | Theoretical & Mathematical Physics. Jun2026, Vol. 227 Issue 3, p925-936. 12p. |
| Subjects: | Renormalization group, Critical exponents, Conformal field theory, Asymptotic expansions |
| Abstract: | We investigate the model using the renormalization group method and the expansion. This model is used in a situation where the coefficients , , and the coefficient of the term depend on two parameters and , and there is a point () at which and are zero. This point is called the tricritical point. The description of the system depends on the trajectory leading to the tricritical point on the plane (). Along trajectories where approaches zero sufficiently fast, the asymptotic description is defined by the interaction and thus the term can be considered as a composite operator. In this case, the logarithmic dimension is , and the expansion is carried out in the dimension. The main exponents of the tricritical model have been calculated in the third order of the expansion. Taking into account the interaction, we were able to calculate the parameter that determines the required decay rate of to implement the tricritical behavior. The tricritical dimensions of the composite operators for have been computed. The resulting values are compared to those known from a conformal field theory and nonperturbative renormalization group. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Six-loop renormalization group analysis of the model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Adzhemyan%2C+L%2E+Ts%2E%22">Adzhemyan, L. Ts.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kompaniets%2C+M%2E+V%2E%22">Kompaniets, M. V.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> mkompan@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Trenogin%2C+A%2E+V%2E%22">Trenogin, A. V.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Jun2026, Vol. 227 Issue 3, p925-936. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Renormalization+group%22">Renormalization group</searchLink><br /><searchLink fieldCode="DE" term="%22Critical+exponents%22">Critical exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Conformal+field+theory%22">Conformal field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We investigate the model using the renormalization group method and the expansion. This model is used in a situation where the coefficients , , and the coefficient of the term depend on two parameters and , and there is a point () at which and are zero. This point is called the tricritical point. The description of the system depends on the trajectory leading to the tricritical point on the plane (). Along trajectories where approaches zero sufficiently fast, the asymptotic description is defined by the interaction and thus the term can be considered as a composite operator. In this case, the logarithmic dimension is , and the expansion is carried out in the dimension. The main exponents of the tricritical model have been calculated in the third order of the expansion. Taking into account the interaction, we were able to calculate the parameter that determines the required decay rate of to implement the tricritical behavior. The tricritical dimensions of the composite operators for have been computed. The resulting values are compared to those known from a conformal field theory and nonperturbative renormalization group. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S0040577926060012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 925 Subjects: – SubjectFull: Renormalization group Type: general – SubjectFull: Critical exponents Type: general – SubjectFull: Conformal field theory Type: general – SubjectFull: Asymptotic expansions Type: general Titles: – TitleFull: Six-loop renormalization group analysis of the model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Adzhemyan, L. Ts. – PersonEntity: Name: NameFull: Kompaniets, M. V. – PersonEntity: Name: NameFull: Trenogin, A. V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00405779 Numbering: – Type: volume Value: 227 – Type: issue Value: 3 Titles: – TitleFull: Theoretical & Mathematical Physics Type: main |
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