Existence of a tricritical point for the Blume-Capel model on $\mathbb{Z}^d$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909239556964352 |
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| author | Gunaratnam, Trishen S. Krachun, Dmitrii Panagiotis, Christoforos |
| author_facet | Gunaratnam, Trishen S. Krachun, Dmitrii Panagiotis, Christoforos |
| contents | We prove the existence of a tricritical point for the Blume-Capel model on $\mathbb{Z}^d$ for every $d\geq 2$. The proof in $d\geq 3$ relies on a novel combinatorial mapping to an Ising model on a larger graph, the techniques of Aizenman, Duminil-Copin, and Sidoravicious (Comm. Math. Phys, 2015), and the celebrated infrared bound. In $d=2$, the proof relies on a quantitative analysis of crossing probabilities of the dilute random cluster representation of the Blume-Capel. In particular, we develop a quadrichotomy result in the spirit of Duminil-Copin and Tassion (Moscow Math. J., 2020), which allows us to obtain a fine picture of the phase diagram in $d=2$, including asymptotic behaviour of correlations in all regions. Finally, we show that the techniques used to establish subcritical sharpness for the dilute random cluster model extend to any $d\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13394 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence of a tricritical point for the Blume-Capel model on $\mathbb{Z}^d$ Gunaratnam, Trishen S. Krachun, Dmitrii Panagiotis, Christoforos Probability Mathematical Physics 60K35, 82B43 We prove the existence of a tricritical point for the Blume-Capel model on $\mathbb{Z}^d$ for every $d\geq 2$. The proof in $d\geq 3$ relies on a novel combinatorial mapping to an Ising model on a larger graph, the techniques of Aizenman, Duminil-Copin, and Sidoravicious (Comm. Math. Phys, 2015), and the celebrated infrared bound. In $d=2$, the proof relies on a quantitative analysis of crossing probabilities of the dilute random cluster representation of the Blume-Capel. In particular, we develop a quadrichotomy result in the spirit of Duminil-Copin and Tassion (Moscow Math. J., 2020), which allows us to obtain a fine picture of the phase diagram in $d=2$, including asymptotic behaviour of correlations in all regions. Finally, we show that the techniques used to establish subcritical sharpness for the dilute random cluster model extend to any $d\geq 2$. |
| title | Existence of a tricritical point for the Blume-Capel model on $\mathbb{Z}^d$ |
| topic | Probability Mathematical Physics 60K35, 82B43 |
| url | https://arxiv.org/abs/2210.13394 |