Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models
The Landau-Wilson field theory with O(n)×O(m) symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in 4−ε dimensions within the minimal subtraction scheme in the six-loop approximation. The ε expansions for marginal di...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-01-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321319303608 |
| _version_ | 1819149755948728320 |
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| author | M.V. Kompaniets A. Kudlis A.I. Sokolov |
| author_facet | M.V. Kompaniets A. Kudlis A.I. Sokolov |
| author_sort | M.V. Kompaniets |
| collection | DOAJ |
| description | The Landau-Wilson field theory with O(n)×O(m) symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in 4−ε dimensions within the minimal subtraction scheme in the six-loop approximation. The ε expansions for marginal dimensionalities of the order parameter nH(m,4−ε), n−(m,4−ε), n+(m,4−ε) separating different regimes of critical behavior are extended up to ε5 terms. Concrete series with coefficients in decimals are presented for m={2,…,6}. The diagram of stability of nontrivial fixed points, including the chiral one, in (m,n) plane is constructed by means of summing up of corresponding ε expansions using various resummation techniques. Numerical estimates of the chiral critical exponents for several couples {m,n} are also found. Comparative analysis of our results with their counterparts obtained earlier within the lower-order approximations and by means of alternative approaches is performed. It is confirmed, in particular, that in physically interesting cases n=2,m=2 and n=2,m=3 phase transitions into chiral phases should be first-order. |
| first_indexed | 2024-12-22T14:06:39Z |
| format | Article |
| id | doaj.art-8e394571f270498ea7075b4840be76eb |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-22T14:06:39Z |
| publishDate | 2020-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-8e394571f270498ea7075b4840be76eb2022-12-21T18:23:17ZengElsevierNuclear Physics B0550-32132020-01-01950Six-loop ε expansion study of three-dimensional O(n)×O(m) spin modelsM.V. Kompaniets0A. Kudlis1A.I. Sokolov2Saint Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg, 199034, RussiaCorresponding author.; Saint Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg, 199034, RussiaSaint Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg, 199034, RussiaThe Landau-Wilson field theory with O(n)×O(m) symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in 4−ε dimensions within the minimal subtraction scheme in the six-loop approximation. The ε expansions for marginal dimensionalities of the order parameter nH(m,4−ε), n−(m,4−ε), n+(m,4−ε) separating different regimes of critical behavior are extended up to ε5 terms. Concrete series with coefficients in decimals are presented for m={2,…,6}. The diagram of stability of nontrivial fixed points, including the chiral one, in (m,n) plane is constructed by means of summing up of corresponding ε expansions using various resummation techniques. Numerical estimates of the chiral critical exponents for several couples {m,n} are also found. Comparative analysis of our results with their counterparts obtained earlier within the lower-order approximations and by means of alternative approaches is performed. It is confirmed, in particular, that in physically interesting cases n=2,m=2 and n=2,m=3 phase transitions into chiral phases should be first-order.http://www.sciencedirect.com/science/article/pii/S0550321319303608 |
| spellingShingle | M.V. Kompaniets A. Kudlis A.I. Sokolov Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models Nuclear Physics B |
| title | Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models |
| title_full | Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models |
| title_fullStr | Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models |
| title_full_unstemmed | Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models |
| title_short | Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models |
| title_sort | six loop ε expansion study of three dimensional o n o m spin models |
| url | http://www.sciencedirect.com/science/article/pii/S0550321319303608 |
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