Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E-7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, sigma(x) and sigma'(x), in either phase are accompanied by associated disorder operators, mu(x ) and mu'(x). Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For sigma(x) and sigma'(x), the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest Z(2) odd particles. Similarly, the equations for mu(x) and mu'(x) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for sigma(x)/sigma'(x) are fixed in terms of those for mu(x)/mu'(x). We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the Delta-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.