A strong-weak duality for the 1d long-range Ising model
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| Format: | Preprint |
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2025
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| _version_ | 1866910010326384640 |
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| author | Benedetti, Dario Lauria, Edoardo Mazac, Dalimil van Vliet, Philine |
| author_facet | Benedetti, Dario Lauria, Edoardo Mazac, Dalimil van Vliet, Philine |
| contents | We investigate the one-dimensional Ising model with long-range interactions decaying as $1/r^{1+s}$. In the critical regime, for $1/2 \leq s \leq 1$, this system realizes a family of nontrivial one-dimensional conformal field theories (CFTs), whose data vary continuously with $s$. For $s>1$ the model has instead no phase transition at finite temperature, as in the short-range case. In the standard field-theoretic description, involving a generalized free field with quartic interactions, the critical model is weakly coupled near $s=1/2$ but strongly coupled in the vicinity of the short-range crossover at $s=1$. We introduce a dual formulation that becomes weakly coupled as $s \to 1$. Precisely at $s=1$, the dual description becomes an exactly solvable conformal boundary condition of the two-dimensional free scalar. We present a detailed study of the dual model and demonstrate its effectiveness by computing perturbatively the CFT data near $s=1$, up to next-to-next-to-leading order in $1-s$, by two independent approaches: (i) standard renormalization of our dual field-theoretic description and (ii) the analytic conformal bootstrap. The two methods yield complete agreement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A strong-weak duality for the 1d long-range Ising model Benedetti, Dario Lauria, Edoardo Mazac, Dalimil van Vliet, Philine High Energy Physics - Theory Statistical Mechanics Mathematical Physics We investigate the one-dimensional Ising model with long-range interactions decaying as $1/r^{1+s}$. In the critical regime, for $1/2 \leq s \leq 1$, this system realizes a family of nontrivial one-dimensional conformal field theories (CFTs), whose data vary continuously with $s$. For $s>1$ the model has instead no phase transition at finite temperature, as in the short-range case. In the standard field-theoretic description, involving a generalized free field with quartic interactions, the critical model is weakly coupled near $s=1/2$ but strongly coupled in the vicinity of the short-range crossover at $s=1$. We introduce a dual formulation that becomes weakly coupled as $s \to 1$. Precisely at $s=1$, the dual description becomes an exactly solvable conformal boundary condition of the two-dimensional free scalar. We present a detailed study of the dual model and demonstrate its effectiveness by computing perturbatively the CFT data near $s=1$, up to next-to-next-to-leading order in $1-s$, by two independent approaches: (i) standard renormalization of our dual field-theoretic description and (ii) the analytic conformal bootstrap. The two methods yield complete agreement. |
| title | A strong-weak duality for the 1d long-range Ising model |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2509.05250 |