Characterization of Lee-Yang polynomials
| dc.creator | Ruelle, David | |
| dc.date | 2008-11-09 | |
| dc.date.accessioned | 2026-07-07T10:17:07Z | |
| dc.date.available | 2026-07-07T10:17:07Z | |
| dc.description | The Lee-Yang circle theorem describes complex polynomials of degree $n$ in $z$ with all their zeros on the unit circle $|z|=1$. These polynomials are obtained by taking $z_1=...=z_n=z$ in certain multiaffine polynomials $Ψ(z_1,...,z_n)$ which we call Lee-Yang polynomials (they do not vanish when $|z_1|,...,|z_n|<1$ or $|z_1|,...,|z_n|>1$). We characterize the Lee-Yang polynomials $Ψ$ in $n+1$ variables in terms of polynomials $Φ$ in $n$ variables (those such that $Φ(z_1,...,z_n)\ne0$ when $|z_1|,...,|z_n|<1$). This characterization gives us a good understanding of Lee-Yang polynomials and allows us to exhibit some new examples. In the physical situation where the $Ψ$ are temperature dependent partition functions, we find that those $Ψ$ which are Lee-Yang polynomials for all temperatures are precisely the polynomials with pair interactions originally considered by Lee and Yang. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0811.1327 | |
| dc.identifier | http://arxiv.org/abs/0811.1327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173747 | |
| dc.subject | Mathematical Physics | |
| dc.title | Characterization of Lee-Yang polynomials | |
| dc.type | text |