The Riemann surface of the chiral Potts model free energy function
| dc.creator | Baxter, R. J. | |
| dc.date | 2002-12-03 | |
| dc.date.accessioned | 2026-07-07T02:48:32Z | |
| dc.date.available | 2026-07-07T02:48:32Z | |
| dc.description | In a recent paper we derived the free energy or partition function of the $N$-state chiral Potts model by using the infinite lattice ``inversion relation'' method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site $T_{pq}$ of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of $T_{pq}$. In terms of the $t_p, t_q$ variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a $(2N-1)$-dimensional lattice (for $N > 2$). The function $T_{pq}$ is meromorphic on this surface: we obtain the orders of all the zeros and poles. For $N$ odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For $N$ even, this method does not give the orders uniquely, but leaves only $[(N+4)/4]$ parameters to be determined. | |
| dc.description | 16 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0212076 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0212076 | |
| dc.identifier | J.Statist.Phys. 112 (2003) 1-26 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/20441 | |
| dc.subject | Statistical Mechanics | |
| dc.title | The Riemann surface of the chiral Potts model free energy function | |
| dc.type | text |