Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911538241077248 |
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| author | Manashov, Alexander N. Shumilov, Leonid A. |
| author_facet | Manashov, Alexander N. Shumilov, Leonid A. |
| contents | We calculate the correction exponents in the chiral Heisenberg model in the $1/N$ expansion. These exponents are related to the slopes of $β$ functions at the phase transition point. We present the results at order $1/N^2$ and check that they agree with the results of the $ε$ expansion near $d = 4$. We find that one of the correction exponents diverges as $d \to 3$. We argue that the appearance of the pole is a rather general phenomenon and is associated with operator mixing involving the system of four-fermion operators. After analyzing the operator mixing structure, we propose a resummation procedure which modifies the exponents already at leading order. We also perform calculations directly in the three-dimensional model and find complete agreement with the resummed exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing Manashov, Alexander N. Shumilov, Leonid A. High Energy Physics - Theory Strongly Correlated Electrons We calculate the correction exponents in the chiral Heisenberg model in the $1/N$ expansion. These exponents are related to the slopes of $β$ functions at the phase transition point. We present the results at order $1/N^2$ and check that they agree with the results of the $ε$ expansion near $d = 4$. We find that one of the correction exponents diverges as $d \to 3$. We argue that the appearance of the pole is a rather general phenomenon and is associated with operator mixing involving the system of four-fermion operators. After analyzing the operator mixing structure, we propose a resummation procedure which modifies the exponents already at leading order. We also perform calculations directly in the three-dimensional model and find complete agreement with the resummed exponents. |
| title | Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.21989 |