The three-state chiral clock model

We give a brief summary of our recent works on the three-state chiral clock model. In these works, we use improved effective field theories with clusters being strips, infinite in the chiral direction and finite in the non-chiral direction. Hence, effective-field transfer matrix methods can be employed in these studies. The effective fields are determined by the Gibbs-Bogoliubov free energy variational principle, leading to Weiss or Bethe approximations in different studies respectively. By systematic improvement of these approximations, i.e. widening the strips, these studies point to the conclusion that there is no Lifshitz point existing at finite non-zero chirality.