14.2. Structure constants Use the modified Coulomb gas to compute the correlation functions of the TIM.

Determine the values of the structure constants given in the text.

14.3. Vacua of the multi-critical Ising model Consider the potential of the multi-critical Ising model V(ϕ) = g1ϕ +g2ϕ2 +g3ϕ3 +g4ϕ4 +g5ϕ5 +g6ϕ6 +ϕ8.

a. Show that, opportunely fine tuning the parameters, the model has a phase with four degenerate vacua.

b. Argue that this is an enough information to conclude that the class of universality of this model does not coincide with the one of the 3-state Potts model, although the two models share the same value of the central charge.