Exact conjectured expressions for correlations in the dense O(1) loop model on cylinders

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 10, 2004, Pages

  Mitra, Saibal ^a   Nienhuis, Bernard ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

correlation functions; integrable spin chains (vertex models); loop models and polymers; percolation problems (theory)

Indexed keywords

EID: 55749101324     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2004/10/P10006     Document Type: Article

References (27)

1. Adamchik V 2001 Symbolic and numeric computation of the Barnes functions Electronic Proc. 7th Int. Conf. on Applications of Computer Algebra (Albuquerque, NM, 31 May-3 June 2001) ed M Wester http://math.unm.edu/ACA/2001/ Proceedings/SymNum/Adamchik-paper.pdf
2. Adamchik V 2001 On the Barnes function Proc. 2001 Int. Symp. on Symbolic and Algebraic Computation (London, Canada, July 2001) (New York: Academic) pp 15-20
3. Andrews G E 1979 Plane partitions (III): The weak Macdonald conjecture Invent. Math. 53 193
4. Barnes E W 1900 The theory of the G-function Quart. J. Math. 31 264
5. Barnes E W 1899 Genesis of the double gamma function Proc. London Math. Soc. 31 358
6. Barnes E W 1901 The theory of the double gamma function Phil. Trans. R. Soc. A 196 265
7. Batchelor M T, de Gier J and Nienhuis B 2001 The quantum symmetric XXZ chain at, alternating-sign matrices and plane partitions J. Phys. A: Math. Gen. 34 L265
8. Baxter R J, Kelland S B and Wu F Y 1976 Equivalence of the Potts model or Whitney polynomial with an ice-type model J. Phys. A: Math. Gen. 9 397
9. Blöte H W J and Nienhuis B 1989 Critical behaviour and conformal anomaly of the O(n) model on the square lattice J. Phys. A: Math. Gen. 22 1415
10. Ciucu M, Eisenkölbl T, Krattenthaler C and Zare D 2001 Enumeration of lozenge tilings of hexagons with a central triangular hole J. Comb. Theory A 95 251
11. David G and Tomei C 1989 The problem of the calissons Am. Math. Monthly 96 429
12. de Gier J 2002 Loops, matchings and alternating-sign matrices Preprint math.CO/0211285
13. den Nijs M P M 1983 Extended scaling relations for the magnetic exponents of the Potts model Phys. Rev. B 27 1674
14. Krattenthaler C 1999 Advanced determinant calculus Séminaire Lotharingien Comb. 42 1-67 (The Andrews Festschrift, paper B42q)
15. Kuperberg G 1996 Another proof of the alternating sign matrix conjecture Int. Math. Res. Notes 139
16. Kuperberg G 2002 Symmetry classes of alternating sign matrices under one roof Ann. Math. 156 835
17. Lunnon W F 1977 The Pascal matrix Fib. Quart. 15 201
18. Mitra S, Nienhuis B, de Gier J and Batchelor M T 2004 Exact expressions for correlations in the ground state of the dense O(1) loop model J. Stat. Mech.: Theor. Exp. P09010
19. Mitra S and Nienhuis B 2003 Osculating random walks on cylinders Discrete Random Walks; DRW'03: Discrete Mathematics and Theoretical Computer Science Proc. AC ed C Banderier and C Krattenthaler p 259
20. Nienhuis B 1984 Coulomb gas description of 2-D critical behaviour J. Stat. Phys. 34 731
21. Nienhuis B 1987 Two-dimensional critical phenomena and the Coulomb gas Phase Transitions and Critical Phenomena vol 11 ed C Domb and J L Lebowitz (New York: Academic)
22. Razumov A V and Stroganov Yu G 2004 Combinatorial nature of ground state vector of O(1) loop model Theor. Math. Phys. 138 333
23. Razumov A V and Stroganov Yu G 2001 O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices Preprint cond-mat/0108103
24. Robbins D P 2000 Symmetry classes of alternating sign matrices Preprint math.CO/0008045
25. Vardi I 1988 Determinants of Laplacians and multiple gamma functions SIAM J. Math. Anal. 19 493
26. Vignéras M F 1979 L'équation fonctionelle de la fonction zêta de Selberg du groupe mudulaire SL(2,) Astérisque 61 235
27. Zeilberger D 1996 Proof of the alternating sign matrix conjecture Electronic J. Combinatorics 3 R13 1-84