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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 38 scientific papers (total in 38 papers)

Integrable models and combinatorics

N. M. Bogolyubovab, K. L. Malysheva

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 (38)
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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
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 5(425), Pages 3–74
DOI: https://doi.org/10.4213/rm9651
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”, Uspekhi Mat. Nauk, 70:5(425) (2015), 3–74; Russian Math. Surveys, 70:5 (2015), 789–856
Citation in format AMSBIB
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    • This publication is cited in the following 38 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:297
    English version PDF:41
    References:80
    First page:63
     
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