Spontaneous magnetization of the superintegrable chiral Potts model: Calculation of the determinant DPQ

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 14, 2010, Pages

  Baxter, R J ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77949769920     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/14/145002     Document Type: Article

References (34)

1. Albertini G, McCoy B M, Perk J H H and Tang S 1989 Excitation spectrum and order parameter for the integrable N-state chiral Potts model Nucl. Phys. B 314 741-63
2. Baxter R J, Perk J H H and Au-Yang H 1988 New solutions of the star-triangle relations for the chiral Potts model Phys. Lett. A 128 138-42
3. Baxter R J 2005 Derivation of the order parameter of the chiral Potts model Phys. Rev. Lett. 94 130602
4. Baxter R J 2005 The order parameter of the chiral Potts model J. Stat. Phys. 120 1-36
5. Baxter R J 1988 The superintegrable chiral Potts model. Phys. Lett. A 133 185-9
6. Baxter R J 1989 Superintegrable chiral Potts model: thermodynamic properties, an 'inverse' model, and a simple associated Hamiltonian J. Stat. Phys. 57 1-39
7. n zero modes Nucl. Phys. B 257 351-70
8. Dolan L and Grady M 1982 Conserved charges from self-duality Phys. Rev. D 25 1587-604
9. Onsager L 1944 Crystal statistics: I. A two-dimensional model with an order-disorder transition Phys. Rev. 65 117-49
10. Au-Yang H and Perk J H H 1989 Onsager's star-triangle equation: master key to integrability Adv. Stud. Pure Math. 19 57-94
11. Davies B 1990 Onsager's algebra and integrability J. Phys. A: Math. Gen. 23 2245-61
12. Davies 1991 Onsager's algebra and the Dolan-Grady condition in the non-self-dual case J. Math. Phys. 32 2945-50
13. von Gehlen G and Roan S S 2001 The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory (NATO Science Series II) vol 35 (Berlin: Springer) pp 155-72 (arXiv:hep-th/0104144)
14. Nishino A and Deguchi T 2008 An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model J. Stat. Phys. 133 587-615
15. 2 generators J. Phys. A: Math. Theor. 41 275201
16. Au-Yang H and Perk J H H 2009 Eigenvectors in the superintegrable model: II. Ground-state sector J. Phys. A: Math. Theor. 42 375208
17. Au-Yang H and Perk J H H 2010 Identities in the superintegrable chiral Potts model J. Phys. A: Math. Theor. 43 025203
18. Au-Yang H and Perk J H H 2010 Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices arXiv:0907.0362
19. Kaufman B and Onsager L 1949 Crystal statistics: III. Short-range order in a binary Ising lattice Phys. Rev. 76 1244-52
20. Yang C N 1952 The spontaneous magnetization of a two-dimensional Ising model Phys. Rev. 85 808-16
21. Montroll E W, Potts R B and Ward J C 1963 Correlations and spontaneous magnetization of the two-dimensional Ising model J. Math. Phys. 4 308-22
22. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic) (reprinted in 2007 by Dover, New York)
23. Baxter R J 2008 Algebraic reduction of the Ising model J. Stat. Phys. 132 959-82
24. Baxter R J 2008 A conjecture for the superintegrable chiral Potts model J. Stat. Phys. 132 983-1000
25. Baxter R J 2009 Some remarks on a generalization of the superintegrable chiral Potts model J. Stat. Phys. 137 798-813
26. Kaufman B 1949 Crystal statistics: II. Partition function evaluated by spinor analysis Phys. Rev. 76 1232-43
27. Onsager L 1949 Discussione e observazioni Proc. of the IUPAP Conf. on Statistical Mechanics Nuovo Cimento (Suppl.) Ser. 9 6 261
28. Onsager L 1971 The Ising model in two dimensions Critical Phenomena in Alloys, Magnets and Superconductors ed R E Mills, E Ascher and R I Jaffee (New York: McGraw-Hill) pp 3-12
29. Krattenthaler C 1998/1999 Advanced determinant calculus Séminaire Lotharingien de Combinatoire vol 42 [B42q] (http://www.mat.univie.ac.at/slc/)
30. Krattenthaler C 2001 The Andrews Festschrift ed D Foata and G-N Han (Berlin: Springer) p 349
31. Noble B 1958 Methods Based on the Wiener-Hopf Technique (London: Pergamon)
32. Grenander U and Szeg G 1958 Toeplitz Forms and their Applications (Berkeley, CA: University of California Press)
33. Iorgov N, Shadura V, Tykhyy Yu, Pakuliak S and von Gehlen G 2009 Spin operator matrix elements in the superintegrable chiral Potts quantum chain arXiv:0912.5027
34. Baxter R J 2010 Proof of the determinantal form of the spontaneous magnetization of the superintegrable chiral Potts model arXiv:1001.0281