Universal amplitude ratios and Coxeter geometry in the dilute A model

Details Universal amplitude ratios and Coxeter geometry in the dilute A model Universal amplitude ratios and Coxeter geometry in the dilute A model

2002-04-10

arxiv.org/abs/cond-mat/0204232v1

Nucl.Phys. B636 (2002) 435-464

Physics

Condensed Matter

Statistical Mechanics

32 pages (tcilatex)

Scientific paper

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 $\phi_{1,2}$ 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 $\phi_{1,2}$ 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, $L=\infty$, we relate the structure of the Bethe roots to the Lie algebras $E_{8,7,6}$ and $D_4$ 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.

Affiliated with

Also associated with

No associations

Rating

Universal amplitude ratios and Coxeter geometry in the dilute A model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Universal amplitude ratios and Coxeter geometry in the dilute A model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universal amplitude ratios and Coxeter geometry in the dilute A model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40093