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

two dimensional water

• modeling freezing water

related items

• Cartan matrices E n
• Temperley-Lieb algebra

encyclopedia

• http://en.wikipedia.org/wiki/Potts_model

books

• Potts model and related problems in statistical mechanics
  • P. Martin

expositions

• Au-Yang, Helen, and Jacques H. H. Perk. “About 30 Years of Integrable Chiral Potts Model, Quantum Groups at Roots of Unity and Cyclic Hypergeometric Functions.” arXiv:1601.01014 [math-Ph], January 5, 2016. http://arxiv.org/abs/1601.01014.
• Perk, Jacques H. H. “The Early History of the Integrable Chiral Potts Model and the Odd-Even Problem.” arXiv:1511.08526 [math-Ph], November 26, 2015. http://arxiv.org/abs/1511.08526.

articles

• Au-Yang, Helen, and Jacques H. H. Perk. “CSOS Models Descending from Chiral Potts Models: Degeneracy of the Eigenspace and Loop Algebra.” arXiv:1511.08523 [cond-Mat, Physics:math-Ph], November 26, 2015. http://arxiv.org/abs/1511.08523.
• Jacobsen, Jesper Lykke. “Critical Points of Potts and O(\(N\)) Models from Eigenvalue Identities in Periodic Temperley-Lieb Algebras.” arXiv:1507.03027 [cond-Mat, Physics:math-Ph], July 10, 2015. http://arxiv.org/abs/1507.03027.
• Lencses, M., and G. Takacs. “Confinement in the Q-State Potts Model: An RG-TCSA Study.” arXiv:1506.06477 [cond-Mat, Physics:hep-Th], June 22, 2015. http://arxiv.org/abs/1506.06477.
• 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