On the Kertész line: Some rigorous bounds
| dc.creator | Ruiz, Jean | |
| dc.creator | Wouts, Marc | |
| dc.date | 2008-02-13 | |
| dc.date.accessioned | 2026-07-07T09:39:18Z | |
| dc.date.available | 2026-07-07T09:39:18Z | |
| dc.description | We study the Kertész line of the $q$--state Potts model at (inverse) temperature $β$, in presence of an external magnetic field $h$. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kertész line $h_K (β)$ coincides with the line of first order phase transition for small fields when $q$ is large enough. Here we prove that the first order phase transition implies a jump in the density of the infinite cluster, hence the Kertész line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that $h_K (β)$ equals $\log (q - 1) - \log (β- β_p)$ to the leading order, as $β$ goes to $β_p = - \log (1 - p_c)$ where $p_c$ is the threshold for bond percolation. | |
| dc.description | 11 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0802.1826 | |
| dc.identifier | http://arxiv.org/abs/0802.1826 | |
| dc.identifier | Journal of Mathematical Physics 49 (2008) 053303 | |
| dc.identifier | doi:10.1063/1.2924322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161119 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.title | On the Kertész line: Some rigorous bounds | |
| dc.type | text |