Holomorphic Parafermions in the Potts model and SLE

Details Holomorphic Parafermions in the Potts model and SLE Holomorphic Parafermions in the Potts model and SLE

2006-08-22

arxiv.org/abs/cond-mat/0608496v3

J.Stat.Mech.0612:P12001,2006

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1742-5468/2006/12/P12001

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.

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