Critical threshold for weakly interacting log-correlated focusing Gibbs measures
| Autor: | Greco, Damiano, Oh, Tadahiro, Tao, Liying, Tolomeo, Leonardo |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study log-correlated Gibbs measures on the $d$-dimensional torus with weakly interacting focusing quartic potentials whose coupling constants tend to $0$ as we remove regularization. In particular, we exhibit a phase transition for this model by identifying a critical threshold, separating the weakly and strongly coupling regimes; in the weakly coupling regime, we show that the frequency-truncated measures converge to the base Gaussian measure (possibly with a renormalized $L^2$-cutoff), whereas, in the strongly coupling regime, we prove non-convergence of the frequency-truncated measures, even up to a subsequence. Our result answers an open question posed by Brydges and Slade (1996). Comment: 15 pages |
| Databáze: | arXiv |
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