Holomorphic Parafermions in the Potts model and SLE

Abstract

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 generalisation of the massive Majorana fermion equation. We also compare the parafermionic scaling dimensions with known results from CFT and Coulomb gas methods in the continuum. Finally, we show that expectation values of these parafermions correspond to local observables of the SLE process which is conjectured to describe the scaling limit of the Q-state Potts model.

18 pages. v2: references to related work clarified. v3: minor corrections, version accepted for publication in JSTAT

References in corpus (3)

• Discrete Riemann Surfaces and the Ising model
• Identification of the stress-energy tensor through conformal restriction in SLE and related processes
• Towards conformal invariance of 2D lattice models

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