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

Abstract

It was recently suggested — based on general self-consistency arguments as well as results from the bootstrap [1,2,3] — that the CFT describing the Q-state Potts model is logarithmic for generic values of Q, with rank-two Jordan blocks for L₀ and \( {\overline{L}}_0 \) 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 [2, 3]) very challenging. This problem is solved in the present paper (which can be considered a companion to [2]), and the conjectured logarithmic structure of the CFT confirmed in detail by the study of the lattice model and associated “emerging Jordan blocks.”