Q-states Potts model and Ashkin-Teller model

introduction

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered
Potts model is the spin model for which the Boltzmann weights depend only on whether the two atoms are in the same state or not.
2-states Potts model = Ising model M(3,4) minimal model
3-states Potts model = M(5,6) minimal model
recent developments of superintegrable chiral Potts model
types
- self-dual potts model
- chiral potts model

Molkaraie, Mehdi, and Vicenc Gomez. ‘Efficient Monte Carlo Methods for the Potts Model at Low Temperature’. arXiv:1506.07044 [physics, Stat], 23 June 2015. http://arxiv.org/abs/1506.07044.
Ikhlef, Yacine, and Robert Weston. ‘Discrete Holomorphicity in the Chiral Potts Model’. arXiv:1502.04944 [cond-Mat, Physics:hep-Th, Physics:math-Ph], 17 February 2015. http://arxiv.org/abs/1502.04944.
Dasu, Shival, and Matilde Marcolli. “Potts Models with Magnetic Field: Arithmetic, Geometry, and Computation.” arXiv:1412.7925 [math-Ph], December 26, 2014. http://arxiv.org/abs/1412.7925.
Qin, M. P., Q. N. Chen, Z. Y. Xie, J. Chen, J. F. Yu, H. H. Zhao, B. Normand, and T. Xiang. ‘Partial Long-Range Order in Antiferromagnetic Potts Models’. Physical Review B 90, no. 14 (21 October 2014). doi:10.1103/PhysRevB.90.144424.
The Potts model
- Fa-Yueh Wu, Rev. Mod. Phys. 54, 235 - 268 (1982)
Critical exponents of two-dimensional Potts and bond percolation models
- H W J Blote , M P Nightingale and B Derrida, 1981
Some Exact Results for the Ashkin-Teller Model
- Temperley, H. N. V.; Ashley, Susan E, 1979