Holomorphic parafermions in the Potts model and stochastic Loewner evolution

We analyse parafermionic operators in the Q-state Potts model from three different perspectives. First, we explicitly construct lattice holomorphic observables in the Fortuin–Kasteleyn representation, and point out some special simplifying features of the particular case Q = 2 (Ising model). In particular, away from criticality, we find a lattice generalization of the massive Majorana fermion equation. We also compare the parafermionic scaling dimensions with known results from conformal field theory and Coulomb gas methods in the continuum. Finally, we show that expectation values of these parafermions correspond to local observables of the stochastic Loewner evolution process which is conjectured to describe the scaling limit of the Q-state Potts model.