The random cluster model and new summation and integration identities
| dc.creator | Chen, L. C. | |
| dc.creator | Wu, F. Y. | |
| dc.date | 2005-01-11 | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T06:25:55Z | |
| dc.date.available | 2026-07-07T06:25:55Z | |
| dc.description | We explicitly evaluate the free energy of the random cluster model at its critical point for 0 < q < 4 using an exact result due to Baxter, Temperley and Ashley. It is found that the resulting expression assumes a form which depends on whether $π/2\cos^{-1}[\sqrt(q)/2]$ is a rational number, and if it is a rational number whether the denominator is an odd integer. Our consideration leads to new summation identities and, for q = 2, a closed-form evaluation of the integral [1/(4π^2)] \int_0^{2π}dx \int_0^{2π}dy ln[A + B + C - A cos x - B cos y - C cos(x + y)] = -\ln(2S) + (2/π)[Ti_2(AS) + Ti_2(BS) + Ti_2(CS)], where A, B, C >=0 and S = 1/\sqrt{AB+BC+CA}. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0501228 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0501228 | |
| dc.identifier | J. Phys. A: Math. Gen. 38, 6271-6276 (2005). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96967 | |
| dc.subject | Statistical Mechanics | |
| dc.title | The random cluster model and new summation and integration identities | |
| dc.type | text |