6 research outputs found
Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model
The exact perturbation approach is used to derive the elementary correlation
lengths and related mass gaps of the two-dimensional dilute A_L
lattice model in regimes 1 and 2 for L odd from the Bethe Ansatz solution. In
regime 2 the A_3 model is the E_8 lattice realisation of the two-dimensional
Ising model in a magnetic field at T=T_c. The calculations for the A_3 model in
regime 2 start from the eight thermodynamically significant string types found
in previous numerical studies. These string types are seen to be consistent in
the ordered high field limit. The eight masses obtained reduce with the
approach to criticality to the E_8 masses predicted by Zamolodchikov, thus
providing a further direct lattice determination of the E_8 mass spectrum.Comment: 57 pages, Latex, Elsevier style file
Universal amplitude ratios and Coxeter geometry in the dilute A model
The leading excitations of the dilute model in regime 2 are considered
using analytic arguments. The model can be identified with the integrable
perturbation of the unitary minimal series . 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 perturbation do in terms of trigonometric
functions. In particular, the bootstrap equation corresponding to a self-fusing
process is recovered. For the special cases 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, , we relate the structure of the Bethe roots to the Lie
algebras and 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 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.Comment: 32 pages (tcilatex