Emerging Jordan blocks in the two-dimensional Potts and loop models at generic Q

It was recently suggested – based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) – that the CFT describing the Q-state Potts model is logarithmic for generic values of Q, with rank-two Jordan blocks for L_0 and 1.5mu-1.5mu L-1.5mu 1.5mu_0 in many sectors of the theory. This is despite the well-known fact that the lattice transfer matrix (or Hamiltonian) is diagonalizable in (arbitrary) finite size. While the emergence of Jordan blocks only in the limit L→∞ is perfectly possible conceptually, diagonalizability in finite size makes the measurement of logarithmic couplings (whose values are analytically predicted in arXiv:2007.11539, arXiv:2007.04190) very challenging. This problem is solved in the present paper (which can be considered a companion to arXiv:2007.11539), and the conjectured logarithmic structure of the CFT confirmed in detail by the study of the lattice model and associated "emerging Jordan blocks."