Factorized finite-size Ising model spin matrix elements from separation of variables

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 30, 2009, Pages

  Von Gehlen, G ^a   Iorgov, N ^b   Pakuliak, S ^c,d   Shadura, V ^b  

^a UNIVERSITY OF BONN   (Germany)

^b BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

^c JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^d INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449623058     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/30/304026     Document Type: Article

References (54)

1. Onsager L 1944 Crystal statistics. I. A two-dimensional model with an order-disorder Transition Phys. Rev. 65 117-49
2. Onsager L 1944 Nuovo Cimento (Suppl.) 6 261
3. Yang C N 1952 The spontaneous magnetization of a two-dim. Ising model Phys. Rev. 85 808-16
4. Kaufman B 1949 Crystal Statistics: II. Partition function evaluated by spinor analysis Phys. Rev. 76 1232
5. 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
6. McCoy B M and Wu T T 1973 The Two-dimensional Ising Model (Cambridge: Harward University Press)
7. Wu T T, McCoy B M, Tracy C A and Barouch E 1976 Spin-spin correlation functions for the two-dimensional Ising model: exact theory in the scaling region Phys. Rev. B 13 316-74
8. Palmer J 2007 Planar Ising correlations Progress in Mathematics and Physics vol 49 (Boston: Birkhäuser)
9. McCoy B M 1995 The connection between statistical mechanics and quantum field theory Statistical Mechanics and Field Theory ed V V Bazhanov and C J Burden (Singapore: World Scientific) pp 26-128
10. Perk J H H and Au-Yang H 2009 New results for the correlation functions of the Ising model and the transverse Ising chain arXiv:0901.1931
11. Baxter R J and Enting I G 1978 399th solution of the Ising model J. Phys. A: Math. Gen. 11 2463
12. Baxter R J 2008 Algebraic reduction of the Ising model arXiv:0803.4036 [cond-mat.stat-mech]
13. c Phys. Rev. Lett. 31 1409-11
14. Berg B, Karowski M and Weisz P 1979 Construction of Green's functions from an exact S matrix Phys. Rev. D 19 2477-9
15. Fonseca P and Zamolodchikov A A 2003 Ising field theory in a magnetic field: analytic properties of the free energy J. Stat. Phys. 110 527-90
16. Altshuler B L, Konik R M and Tsvelik A M 2006 Low temperature correlation functions in integrable models: derivation of the large distance and time asymptotics from the form factor expansion Nucl. Phys. B 739 311-27
17. Schuricht D and Essler F H L 2007 Dynamical response functions in the quantum Ising chain with a boundary J. Stat. Mech.: Theor. Exp. P11004
18. Bugrij A and Lisovyy O 2003 Spin matrix elements in 2D Ising model on the finite lattice Phys. Lett. A 319 390
19. (arXiv:0708.3625) [nlin.SI] - ref-separator -
20. Bugrij A and Lisovyy O 2003 Correlation function of the two-dimensional Ising model on a finite lattice: II J. Theor. Math. Phys. 140 987 (arXiv:0708.3643 [nlin.SI])
21. Sklyanin E K 1990 Functional Bethe ansatz Integrable and Superintegrable Systems ed B A Kupershmidt (Singapore: World Scientific) pp 8-33
22. Sklyanin E K 1992 Quantum inverse scattering method: selected topics Quantum Group and Quantum Integrable Systems (Nankai Lectures in Math. Phys.) ed Ge Mo-Lin (Singapore: World Scientific) pp 63-97
23. Kharchev S and Lebedev D 1999 Integral representations for the eigenfunctions of a quantum periodic Toda chain Lett. Math. Phys. 50 53-77
24. Kharchev S and Lebedev D 2000 Eigenfunctions of Toda chain: the Mellin-Barnes representation JETP Lett. 71 235-8
25. Tarasov V O 1992 Cyclic monodromy matrices for the R-matrix of the six-vertex model and the chiral Potts model with fixed spin boundary conditions Proc. RIMS Research Project 91 on Infinite Analysis (1991) 1-13 Int. J. Mod. Phys. A 7 (Suppl. 1B) 963-75
26. 2-model for N = 2 J. Phys. A: Math. Gen. 39 2265-85 arXiv:nlin.SI/0512026
27. von Gehlen G, Iorgov N, Pakuliak S and Shadura V 2006 The Baxter-Bazhanov-Stroganov model: separation of variables and the Baxter equation J. Phys. A: Math. Gen. 39 7257-82
28. von Gehlen G, Iorgov N, Pakuliak S, Shadura V and Tykhyy Yu 2007 Form-factors in the finite size Baxter-Bazhanov-Stroganov model: I. Norms and matrix elements J. Phys. A: Math. Theor. 40 14117-38
29. von Gehlen G, Iorgov N, Pakuliak S, Shadura V and Tykhyy Yu 2008 Form-factors in the Baxter-bazhanov-Stroganov model II: Ising model on the finite lattice J. Phys. A: Math. Theor. 41 095003
30. Baxter R J 1989 Superintegrable chiral Potts model: thermodynamic properties, an 'Inverse' model, and a simple associated Hamiltonian J. Stat. Phys. 57 1-39
31. Bazhanov V V and Stroganov Yu G 1990 Chiral Potts model as a descendant of the six-vertex model J. Stat. Phys. 59 799-817
32. Korepanov I G 1987 Hidden symmetries in the 6-vertex model Chelyabinsk Polytechnical Institute, archive VINITI No. 1472-V87 (in Russian)
33. Korepanov I G 1994 Hidden symmetries in the 6-vertex model of Statistical Physics Zapiski Nauchn. Semin. POMI 215 163-77 (arXiv:hep-th/9410066)
34. 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
35. Baxter R J 1990 Chiral Potts model: eigenvalues of the transfer matrix Phys. Lett. A 146 110-14
36. Baxter R J, Bazhanov V V and Perk J H H 1990 Functional relations for the transfer matrices of the Chiral Potts model Int. J. Mod. Phys. B 4 803-69
37. 2 generators J. Phys. A: Math. Theor. 41 275201 (arXiv:0710.5257 [math-ph])
38. Au-Yang H and Perk J H H 2008 Eigenvectors in the superintegrable model: II. Ground state sector arXiv:0803.3029 [math-ph]
39. Iorgov N 2006 Eigenvectors of open Bazhanov-Stroganov quantum chain SIGMA 2 (19) 10
40. q) model with fixed-spin boundary conditions Theor. Math. Phys. 155 585-97
41. 2) J. Stat. Mech. P09021
42. q) model J. Stat. Phys. 117 1-25
43. Tarasov V O 1990 Transfer matrix of the superintegrable Chiral Potts model. Bethe ansatz spectrum Phys. Lett. A 147 487-90
44. 2) J. Phys. A: Math. Theor. 42 072003 (arXiv:0806.0216 [cond-mat.stat-mech])
45. 2 model for N = 2 JETP Lett. 82 311-5
46. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic)
47. Bazhanov V V and Baxter R J 1992 New solvable lattice models in three dimensions J. Stat. Phys. 69 453-85
48. Kulish P P and Sklyanin E K 1982 Lecture Notes in Physics 151 (Berlin: Springer) p 61
49. Kirillov A N and Reshetikhin N Yu 1987 Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum J. Phys. A: Math. Gen. 20 1565
50. Bazhanov V V and Reshetikhin N Yu 1989 Critical RSOS models and conformal field theory Int. J. Mod. Phys. A 4 115
51. Maillet J M and Terras V 2000 On the quantum inverse scattering problem Nucl. Phys. B 575 627-44
52. (2)- model and root-of-unity symmetry of the XXZ spin chain of higher spin J. Phys. A: Math. Theor. 40 1481-512 arXiv:cond-mat/0607258
53. Kuznetsov V 2002 Inverse problem for sl(2) lattices Symmetry and Perturbation Theory (Cala Gonone, Sardinia: World Scientific) 136-52 (arXiv:nlin/0207025)
54. Babelon O 2003 Equations in dual variables for Whittaker functions Lett. Math. Phys. 65 229-40