Analysis of the 3d massive renormalization group perturbative expansions: a delicate case
The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all mod...
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| Published in: | Condensed Matter Physics |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут фізики конденсованих систем НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/32132 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case / B. Delamotte, M. Dudka, Yu. Holovatch, D. Mouhanna // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43703:1-16. — Бібліогр.: 61 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862554895785132032 |
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| author | Delamotte, B. Dudka, M. Holovatch, Yu. Mouhanna, D. |
| author_facet | Delamotte, B. Dudka, M. Holovatch, Yu. Mouhanna, D. |
| citation_txt | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case / B. Delamotte, M. Dudka, Yu. Holovatch, D. Mouhanna // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43703:1-16. — Бібліогр.: 61 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d = 3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N < Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N) and cubic models. We conclude from this analysis that the stable FP found for N < Nc in frustrated models is spurious. Since Nc > 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.
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| first_indexed | 2025-11-25T22:16:43Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-32132 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-11-25T22:16:43Z |
| publishDate | 2010 |
| publisher | Інститут фізики конденсованих систем НАН України |
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| spelling | Delamotte, B. Dudka, M. Holovatch, Yu. Mouhanna, D. 2012-04-09T21:32:26Z 2012-04-09T21:32:26Z 2010 Analysis of the 3d massive renormalization group perturbative expansions: a delicate case / B. Delamotte, M. Dudka, Yu. Holovatch, D. Mouhanna // Condensed Matter Physics. — 2010. — Т. 13, № 4. — С. 43703:1-16. — Бібліогр.: 61 назв. — англ. 1607-324X PACS: 75.10.Hk, 11.10.Hi, 12.38.Cy https://nasplib.isofts.kiev.ua/handle/123456789/32132 The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d = 3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N < Nc, the results obtained at the stable FP are similar to those obtained at the spurious FPs of the O(N) and cubic models. We conclude from this analysis that the stable FP found for N < Nc in frustrated models is spurious. Since Nc > 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order. We thank Prof. A. Prykarpatsky and Prof. D. Sankovich for an invitation to submit a paper to this Festschrift. It is our special pleasure to congratulate Prof. Nikolai N. Bogolubov (Jr.) on the occasion of his jubilee and to wish him many years of fruitful and satisfying scientific activity. We wish to acknowledge the CNRS–NAS Franco-Ukrainian bilateral exchange program. This work was supported in part by the Austrian Fonds zur F¨orderung der wissenschaftlichen Forschung under Project No. P19583–N20. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Analysis of the 3d massive renormalization group perturbative expansions: a delicate case Аналіз 3d масивних розвинень пертурбативної ренормалізаційної групи: делікатна справа Article published earlier |
| spellingShingle | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case Delamotte, B. Dudka, M. Holovatch, Yu. Mouhanna, D. |
| title | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| title_alt | Аналіз 3d масивних розвинень пертурбативної ренормалізаційної групи: делікатна справа |
| title_full | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| title_fullStr | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| title_full_unstemmed | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| title_short | Analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| title_sort | analysis of the 3d massive renormalization group perturbative expansions: a delicate case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/32132 |
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