Phase transitions for fractional $\Phi^3_d$ on the torus
| Title: | Phase transitions for fractional $\Phi^3_d$ on the torus |
|---|---|
| Authors: | Nikov, Niko |
| Publication Year: | 2025 |
| Collection: | Mathematics Mathematical Physics |
| Subject Terms: | Mathematics - Probability, Mathematical Physics, Mathematics - Analysis of PDEs, 60H30 (Primary) 81T08, 82B26, 35Q55 (Secondary) |
| More Details: | We consider the fractional $\Phi^3_d$-measure on the $d$-dimensional torus, with Gaussian free field having inverse covariance $(1-\Delta)^\alpha$, and show a phase transition at $d=3\alpha$. More precisely, in a regular regime $d<3\alpha$, one can construct and normalise this measure, and obtain a measure which is absolutely continuous with respect to the Gaussian free field $\mu$. At $d=3\alpha$, the behaviour depends on the size $|\sigma|$ of the nonlinearity: for $|\sigma|\ll1$, the measure exists, but is singular with respect to $\mu$, whereas for $|\sigma|\gg1$, the measure is not normalisable. This generalises a result of Oh, Okamoto, and Tolomeo (2025) on the $\Phi^3_3$-measure. Comment: 45 pages |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2501.17669 |
| Accession Number: | edsarx.2501.17669 |
| Database: | arXiv |
| Description not available. |