Universal amplitude ratios and Coxeter geometry in the dilute A_L model

Korff, C. and Seaton, K.A. (2002) Universal amplitude ratios and Coxeter geometry in the dilute A_L model. Nuclear Physics B, 636(3), pp. 435-464. (doi: 10.1016/S0550-3213(02)00438-8)

Abstract

The leading excitations of the dilute A_L model in regime 2 are considered using analytic arguments. The model can be identified with the integrable φ_1,2 perturbation of the unitary minimal series M_L,L+1. It is demonstrated that the excitation spectrum of the transfer matrix satisfies the same functional equations in terms of elliptic functions as the exact S-matrices of the φ_1,2 perturbation do in terms of trigonometric functions. In particular, the bootstrap equation corresponding to a self-fusing process is recovered. For the special cases L=3,4,6 corresponding to the Ising model in a magnetic field, and the leading thermal perturbations of the tricritical Ising and three-state Potts model, as well as for the unrestricted model, L=∞, we relate the structure of the Bethe roots to the Lie algebras E_8,7,6 and D₄ using Coxeter geometry. In these cases Coxeter geometry also allows for a single formula in generic Lie algebraic terms describing all four cases. For general L we calculate the spectral gaps associated with the leading excitation which allows us to compute universal amplitude ratios characteristic of the universality class. The ratios are of field theoretic importance as they enter the bulk vacuum expectation value of the energy momentum tensor associated with the corresponding integrable quantum field theories.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Korff, Professor Christian
• Authors: Korff, C., and Seaton, K.A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Nuclear Physics B
• ISSN: 0550-3213
• ISSN (Online): 1873-1562
• Published Online: 17 June 2002