Eigenvalue amplitudes of the Potts model on a torus
| dc.creator | Richard, Jean-Francois | |
| dc.creator | Jacobsen, Jesper Lykke | |
| dc.date | 2006-08-23 | |
| dc.date.accessioned | 2026-07-07T08:26:31Z | |
| dc.date.available | 2026-07-07T08:26:31Z | |
| dc.description | We consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L x N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix T\_L. Using a combinatorial method, we establish the decomposition Z(L,N) = \sum\_{l,D\_k} b^{l,D\_k} K\_{l,D\_k}, where the characters K\_{l,D\_k} = \sum\_i (λ\_i)^N are simple traces. In this decomposition, the amplitudes b^{l,D\_k} of the eigenvalues λ\_i of T\_L are labelled by the number l=0,1,...,L of clusters which are non-contractible with respect to the transfer (N) direction, and a representation D\_k of the cyclic group C\_l. We obtain rigorously a general expression for b^{l,D\_k} in terms of the characters of C\_l, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur. | |
| dc.description | 29 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0608055 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0608055 | |
| dc.identifier | Nuclear Physics B 769 (2007) 256-274 | |
| dc.identifier | doi:10.1016/j.nuclphysb.2007.01.028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136965 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Combinatorics | |
| dc.title | Eigenvalue amplitudes of the Potts model on a torus | |
| dc.type | text |