Discrete holomorphicity in the chiral Potts model

Yacine Ikhlef, Robert Weston*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
54 Downloads (Pure)


We construct lattice parafermions for the Z(N) chiral Potts model in terms of quasi-local currents of the underlying quantum group. We show that the conservation of the quantum group currents leads to twisted discrete-holomorphicity (DH) conditions for the parafermions. At the critical Fateev-Zamolodchikov point the parafermions are the usual ones, and the DH conditions coincide with those found previously by Rajabpour and Cardy. Away from the critical point, we show that our twisted DH conditions can be understood as deformed lattice current conservation conditions for an underlying perturbed conformal field theory in both the general and N = 2 Ising cases.

Original languageEnglish
Article number294001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number29
Publication statusPublished - 24 Jul 2015


  • chiral Potts model
  • discrete holomorphicity
  • exactly solvable lattice models
  • parafermions
  • quantum groups

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability


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