Critical wetting in the (2+1)D Solid-On-Solid model
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909322723721216 |
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| author | Chen, Joseph Gheissari, Reza Lubetzky, Eyal |
| author_facet | Chen, Joseph Gheissari, Reza Lubetzky, Eyal |
| contents | In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $λ_w= \log (\frac{1}{1-e^{-4β}})$. At $λ<λ_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac1{4β}\log n+O(1)$; at $λ>λ_w$ it is localized at some $O(1)$ height. We show that at $λ=λ_w$, there is delocalization, with rigidity now at height $\lfloor \frac1{6β}\log n+\frac13\rfloor$, confirming a conjecture of Lacoin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical wetting in the (2+1)D Solid-On-Solid model Chen, Joseph Gheissari, Reza Lubetzky, Eyal Probability Mathematical Physics 60K35, 82B20, 82B27 In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $λ_w= \log (\frac{1}{1-e^{-4β}})$. At $λ<λ_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac1{4β}\log n+O(1)$; at $λ>λ_w$ it is localized at some $O(1)$ height. We show that at $λ=λ_w$, there is delocalization, with rigidity now at height $\lfloor \frac1{6β}\log n+\frac13\rfloor$, confirming a conjecture of Lacoin. |
| title | Critical wetting in the (2+1)D Solid-On-Solid model |
| topic | Probability Mathematical Physics 60K35, 82B20, 82B27 |
| url | https://arxiv.org/abs/2406.12040 |