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We analyse parafermionic operators in the Q-state Potts model from threedifferent perspectives. First, we explicitly construct lattice holomorphicobservables in the Fortuin-Kasteleyn representation, and point out some specialsimplifying features of the particular case Q=2 (Ising model). In particular,away from criticality, we find a lattice generalisation of the massive Majoranafermion equation. We also compare the parafermionic scaling dimensions withknown results from CFT and Coulomb gas methods in the continuum. Finally, weshow that expectation values of these parafermions correspond to localobservables of the SLE process which is conjectured to describe the scalinglimit of the Q-state Potts model.Comment: 18 pages. v2: references to related work clarified. v3: minor  corrections, version accepted for publication in JSTA

Holomorphic parafermions in the Potts model and stochastic Loewner evolution