Schrodinger equation approach to non-linear $σ$-models in the large N-limit
| dc.creator | Shalaev, Boris N. | |
| dc.date | 1999-12-23 | |
| dc.date.accessioned | 2026-07-07T03:15:46Z | |
| dc.date.available | 2026-07-07T03:15:46Z | |
| dc.description | Non-linear d-dimensional vector $σ$-models are studied in the large N-limit. It is found that a two-point correlation function obeys a standard Schrodinger equation for a free quantum particle moving in the $δ$-function quantum well. The threshold problem for bound states in this equation is shown to be equivalent to a critical behavior of these models above and below the Curie point. The SU(N)- symmetric Ginzburg-Landau (GL) $σ$-model subject to a uniform magnetic field H is considered in the large-N limit within the Schrodinger equation approach. A upper critical magnetic field line $H_{c2}(T)$ of type-II superconductors for an arbitrary external H is obtained without exploiting the lowest Landau level (LLL) approximation. Both low-H perturbation expansion terms and exponentially small corrections to the LLL approximation are calculated. Correspondences between the one-particle quantum mechanics and critical phenomena as well as some applications of the above method to other models of statistical mechanics are also discussed. | |
| dc.description | 16 pages, revtex | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9912424 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9912424 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/30107 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Schrodinger equation approach to non-linear $σ$-models in the large N-limit | |
| dc.type | text |