A. V. Razumov, Yu. G. Stroganov, “Combinatorial Nature of the Ground-State Vector of the $O(1)$ Loop Model”, TMF, 138:3 (2004), 395–400; Theoret. and Math. Phys., 138:3 (2004), 333

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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 138, Number 3, Pages 395–400
DOI: https://doi.org/10.4213/tmf32 (Mi tmf32)

This article is cited in 106 scientific papers (total in 106 papers)

Combinatorial Nature of the Ground-State Vector of the

$O(1)$ Loop Model

A. V. Razumov, Yu. G. Stroganov

Institute for High Energy Physics

Full-text PDF (209 kB) Citations (106)

References:

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DOI: https://doi.org/10.4213/tmf32

Abstract: Studying a possible connection between the ground-state vector for some special spin systems and the so-called alternating-sign matrices, we find numerical evidence that the components of the ground-state vector of the

$O(1)$ loop model coincide with the numbers of the states of the so-called fully packed loop model with fixed pairing patterns. The states of the latter system are in one-to-one correspondence with alternating-sign matrices. This allows advancing the hypothesis that the components of the ground-state vector of the

$O(1)$ loop model coincide with the cardinalities of the corresponding subsets of the alternating-sign matrices. In a sense, our conjecture generalizes the conjecture of Bosley and Fidkowski, which was refined by Cohn and Propp and proved by Wieland.

Keywords: loop model, ground state, fully packed loop model.

Received: 06.05.2003

English version:
Theoretical and Mathematical Physics, 2004, Volume 138, Issue 3, Pages 333–337
DOI: https://doi.org/10.1023/B:TAMP.0000018450.36514.d7

Bibliographic databases:

Language: Russian

Citation: A. V. Razumov, Yu. G. Stroganov, “Combinatorial Nature of the Ground-State Vector of the

$O(1)$ Loop Model”, TMF, 138:3 (2004), 395–400; Theoret. and Math. Phys., 138:3 (2004), 333–337

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/tmf32

https://www.mathnet.ru/eng/tmf/v138/i3/p395

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A M Povolotsky, “Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder: II. Rotated lattice”, J. Stat. Mech., 2023:3 (2023), 033103
Korff Ch., “Cylindric Hecke Characters and Gromov-Witten Invariants Via the Asymmetric Six-Vertex Model”, Commun. Math. Phys., 381:2 (2021), 591–640
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Povolotsky A.M., “Exact Densities of Loops in O(1) Dense Loop Model and of Clusters in Critical Percolation on a Cylinder”, J. Phys. A-Math. Theor., 54:22 (2021), 22LT01
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Povolotsky A.M., “Laws of Large Numbers in the Raise and Peel Model”, J. Stat. Mech.-Theory Exp., 2019, 074003
Aigner F., “Refined Enumerations of Alternating Sign Triangles”, Adv. Appl. Math., 111 (2019), UNSP 101921
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Aigner F., “Fully Packed Loop Configurations: Polynomiality and Nested Arches”, Electron. J. Comb., 25:1 (2018), P1.27
Paul Zinn-Justin, “Loop Models and $K$ -Theory”, SIGMA, 14 (2018), 069, 48 pp.
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Weston R., Yang J., “Lattice Supersymmetry in the Open Xxz Model: An Algebraic Bethe Ansatz Analysis”, J. Stat. Mech.-Theory Exp., 2017, 123104
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Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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