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TMF, 2005, Volume 142, Number 2, Pages 284–292 (Mi tmf1782)  

This article is cited in 24 scientific papers (total in 24 papers)

$O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices

A. V. Razumov, Yu. G. Stroganov

Institute for High Energy Physics

Abstract: This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the $O(1)$ loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the $O(1)$ loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.

Keywords: loop model, ground state, fully packed loop model, alternating-sign matrices

DOI: https://doi.org/10.4213/tmf1782

Full text: PDF file (209 kB)
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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 237–243

Bibliographic databases:


Citation: A. V. Razumov, Yu. G. Stroganov, “$O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices”, TMF, 142:2 (2005), 284–292; Theoret. and Math. Phys., 142:2 (2005), 237–243

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. de Gier J, “Loops, matchings and alternating-sign matrices”, Discrete Mathematics, 298:1–3 (2005), 365–388  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Di Francesco P, “Inhomogeneous loop models with open boundaries”, Journal of Physics A-Mathematical and General, 38:27 (2005), 6091–6120  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Di Francesco, P, “Determinant formulae for some tiling problems and application to fully packed loops”, Annales de l Institut Fourier, 55:6 (2005), 2025  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Di Francesco P, Zinn-Justin P, Zuber JB, “Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P08011  crossref  isi  scopus  scopus
    5. Zinn-Justin P., “Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns”, Electronic Journal of Combinatorics, 13:1 (2006), R110  mathscinet  zmath  isi
    6. Razumov AV, Stroganov YG, Zinn-Justin P, “Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2”, Journal of Physics A-Mathematical and Theoretical, 40:39 (2007), 11827–11847  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Shigechi K, Uchiyama M, “The A(kappa) generalization of the O(1) loop model on a cylinder: affine Hecke algebra, q-KZ equation and the sum rule”, Journal of Physics A-Mathematical and Theoretical, 40:30 (2007), 8923–8957  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Alcaraz FC, Rittenberg V, “Diffferent facets of the raise and peel model”, Journal of Statistical Mechanics-Theory and Experiment, 2007, no. JUL, P07009  crossref  mathscinet  isi  scopus  scopus
    9. Zinn-Justin P, “Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01007  crossref  mathscinet  isi  scopus  scopus
    10. Di Francesco P, “Open boundary quantum Knizhnik–Zamolodchikov equation and the weighted enumeration of plane partitions with symmetries”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01024  crossref  mathscinet  isi  scopus  scopus
    11. Di Francesco P, Zinn-Justin P, “Quantum Knizhnik–Zamolodchikov equation: reflecting boundary conditions and combinatorics”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P12009  crossref  mathscinet  isi  scopus  scopus
    12. Cantini, L, “The rotor model with spectral parameters and enumerations of alternating sign matrices”, Journal of Statistical Mechanics-Theory and Experiment, 2007, no. AUG, P08012  crossref  isi
    13. Beccaria M., “On the supersymmetric vacua of the Veneziano-Wosiek model”, Journal of High Energy Physics, 2007, no. 3, 117  crossref  mathscinet  isi
    14. de Gier, J, “The exact finite size ground state of the O(n=1) loop model with open boundaries”, Journal of Statistical Mechanics-Theory and Experiment, 2009, P04010  crossref  isi  scopus  scopus
    15. J.-Ch. Aval, “The symmetry of the partition function of some square ice models”, Theoret. and Math. Phys., 161:3 (2009), 1582–1589  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    16. Aufgebauer B., Brockmann M., Nuding W., Kluemper A., Sedrakyan A., “The complete conformal spectrum of a sl(2 vertical bar 1) invariant network model and logarithmic corrections”, J Stat Mech Theory Exp, 2010, P12010  crossref  mathscinet  isi  elib  scopus  scopus
    17. Cantini L., Sportiello A., “Proof of the Razumov-Stroganov conjecture”, J Combin Theory Ser A, 118:5 (2011), 1549–1574  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. Ikhlef Ya., Ponsaing A.K., “Finite-Size Left-Passage Probability in Percolation”, J. Stat. Phys., 149:1 (2012), 10–36  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    19. Alcaraz F.C. Rittenberg V., “Nonlocal Growth Processes and Conformal Invariance”, J. Stat. Mech.-Theory Exp., 2012, P05022  crossref  isi  scopus  scopus
    20. Cantini L., “Finite Size Emptiness Formation Probability of the Xxz Spin Chain at Delta =-1/2”, J. Phys. A-Math. Theor., 45:13 (2012), 135207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    21. Aval J.-Ch. Duchon Ph., “Half-Turn Symmetric Fpls with Rare Couplings and Tilings of Hexagons”, Theor. Comput. Sci., 502 (2013), 143–152  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    22. Alcaraz F.C., Rittenberg V., “Nonlocal Asymmetric Exclusion Process on a Ring and Conformal Invariance”, J. Stat. Mech.-Theory Exp., 2013, P09010  crossref  mathscinet  isi  scopus  scopus
    23. Cantini L. Sportiello A., “A One-Parameter Refinement of the Razumov-Stroganov Correspondence”, J. Comb. Theory Ser. A, 127 (2014), 400–440  crossref  mathscinet  zmath  isi  scopus  scopus
    24. Povolotsky A.M., Pyatov P., Rittenberg V., “Large Deviations of Avalanches in the Raise and Peel Model”, J. Stat. Mech.-Theory Exp., 2018, 053107  crossref  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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