N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789

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Russian Mathematical Surveys, 2015, Volume 70, Issue 5, Pages 789–856
DOI: https://doi.org/10.1070/RM2015v070n05ABEH004964 (Mi rm9651)

This article is cited in 40 scientific papers (total in 40 papers)

Integrable models and combinatorics

N. M. Bogolyubov^ab, K. L. Malyshev^a

^a St. Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences
^b St. Petersburg National Research University of Information Technology, Mechanics, and Optics

English version PDF (1414 kB) Citations (40) Russian version article

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DOI: https://doi.org/10.1070/RM2015v070n05ABEH004964

Abstract: Relations between quantum integrable models solvable by the quantum inverse scattering method and some aspects of enumerative combinatorics and partition theory are discussed. The main example is the Heisenberg

$XXZ$ spin chain in the limit cases of zero or infinite anisotropy. Form factors and some thermal correlation functions are calculated, and it is shown that the resulting form factors in a special

$q$ -parametrization are the generating functions for plane partitions and self-avoiding lattice paths. The asymptotic behaviour of the correlation functions is studied in the case of a large number of sites and a moderately large number of spin excitations. For sufficiently low temperature a relation is established between the correlation functions and the theory of matrix integrals.
Bibliography: 125 titles.

Keywords: correlation functions, Heisenberg magnet, four-vertex model, plane partitions, generating functions, symmetric functions.

Funding agency	Grant number
Russian Science Foundation	14-11-00598
This work was supported by the Russian Science Foundation (grant no. 14-11-00598).

Received: 31.01.2015

Bibliographic databases:

Document Type: Article

UDC: 517.958+530.145

PACS: 02.10.Os; 03.65.-w

MSC: Primary 82B20, 37K60, 05E05; Secondary 82B30, 82B41, 82D40, 05C81

Language: English

Original paper language: Russian

Citation: N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856

Citation in format AMSBIB

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Linking options:

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This publication is cited in the following 40 articles:

Tianyu Liu, Xiongxin Yang, “Beyond windability: Approximability of the four-vertex model”, Theoretical Computer Science, 995 (2024), 114491
N. M. Bogoliubov, C. L. Malyshev, “Scalar Product of the Five-Vertex Model and Complete Symmetric Polynomials”, J Math Sci, 2024
N. M. Bogoliubov, C. L. Malyshev, “Semi-infinite Heisenberg XX0 chain and random walks”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 30, Zap. nauchn. sem. POMI, 532, POMI, SPb., 2024, 91–108
N. M. Bogolyubov, C. L. Malyshev, “Scalar product of the five-vertex model and complete symmetric polynomials”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 29, Zap. nauchn. sem. POMI, 520, POMI, SPb., 2023, 124–138
N. M. Bogolyubov, A. G. Pronko, “One-Point Function of the Four-Vertex Model”, J Math Sci, 275:3 (2023), 249
N. M. Bogoliubov, C. L. Malyshev, “Cauchy–Binet Determinantal Identity and Enumeration of Plane Partitions in a High Box”, J Math Sci, 275:3 (2023), 239
I. N. Burenev, “Five-Vertex Model and Lozenge Tilings of a Hexagon with a Dent”, J Math Sci, 275:3 (2023), 271
Belov P., Reshetikhin N., “The Two-Point Correlation Function in the Six-Vertex Model”, J. Phys. A-Math. Theor., 55:15 (2022), 155001
N. M. Bogoliubov, C. L. Malyshev, “Heisenberg XX0 Chain and Random Walks on a Ring”, J Math Sci, 264:3 (2022), 232
C Malyshev, N M Bogoliubov, “Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions”, J. Phys. A: Math. Theor., 55:22 (2022), 225002
I. N. Burenev, A. G. Pronko, “Quantum Hamiltonians Generated by the R-Matrix of the Five-Vertex Model”, J Math Sci, 264:3 (2022), 271
Burenev I.N., Pronko A.G., “Determinant Formulas For the Five-Vertex Model”, J. Phys. A-Math. Theor., 54:5 (2021), 055008
N. M. Bogoliubov, C. L. Malyshev, “Cauchy–Binet determinantal identity and enumeration of plane partitions in a high box”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 25–38
N. M. Bogolyubov, A. G. Pronko, “One-point function of the four-vertex model”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 39–53
I. N. Burenev, “Five-vertex model and lozenge tilings of a hexagon with a dent”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 71–88
Nikolay Bogolyubov, Cyril Malyshev, “How to Draw a Correlation Function”, SIGMA, 17 (2021), 106, 35 pp.
Pozsgay B., Gombor T., Hutsalyuk A., Jiang Yu., Pristyak L., Vernier E., “Integrable Spin Chain With Hilbert Space Fragmentation and Solvable Real-Time Dynamics”, Phys. Rev. E, 104:4 (2021), 044106
M. D. Minin, A. G. Pronko, “Boundary Polarization of the Rational Six-Vertex Model on a Semi-Infinite Lattice”, J Math Sci, 257:4 (2021), 537
N. M. Bogoliubov, “Enumerative Combinatorics of XX0 Heisenberg Chain”, J Math Sci, 257:4 (2021), 459
N. Bogoliubov, C. Malyshev, “The Asymptotics of Plane Partitions with Fixed Volumes of Diagonal Parts”, J Math Sci, 257:4 (2021), 469

Citing articles in Google Scholar: Russian citations, English citations
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References:	102
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