The critical Z-invariant Ising model via dimers: the periodic case
| dc.creator | Boutillier, Cédric | |
| dc.creator | de Tilière, Béatrice | |
| dc.date | 2008-12-19 | |
| dc.date.accessioned | 2026-07-07T12:20:55Z | |
| dc.date.available | 2026-07-07T12:20:55Z | |
| dc.description | We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical square, triangular and honeycomb lattice at the critical temperature. Fisher introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model. We prove that the dimer characteristic polynomial is equal (up to a constant) to the critical Laplacian characteristic polynomial, and defines a Harnack curve of genus 0. We prove an explicit expression for the free energy, and for the Gibbs measure obtained as weak limit of Boltzmann measures. | |
| dc.description | 35 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/0812.3848 | |
| dc.identifier | http://arxiv.org/abs/0812.3848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213206 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B20 | |
| dc.title | The critical Z-invariant Ising model via dimers: the periodic case | |
| dc.type | text |