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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 2, Pages 179–193
DOI: https://doi.org/10.4213/tmf6341 (Mi tmf6341) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Correlation functions of the XX Heisenberg magnet and random walks of vicious walkers

N. M. Bogolyubov, K. L. Malyshev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (499 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf6341
Abstract: We investigate a relation between random walks on a one-dimensional periodic lattice and correlation functions of the XX Heisenberg spin chain. Operator averages over the ferromagnetic state play the role of generating functions of the number of paths traveled by so-called vicious random walkers (vicious walkers annihilate each other if they arrive at the same lattice site). We show that the two-point correlation function of spins calculated over eigenstates of the XX magnet can be interpreted as the generating function of paths traveled by a single walker in a medium characterized by a variable number of vicious neighbors. We obtain answers for the number of paths traveled by the described walker from a fixed lattice site to a sufficiently remote site. We provide asymptotic estimates of the number of paths in the limit of a large number of steps.
Keywords: random walk, Heisenberg magnet, correlation function.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 2, Pages 563–574
DOI: https://doi.org/10.1007/s11232-009-0046-y
Bibliographic databases:
Language: Russian
Citation: N. M. Bogolyubov, K. L. Malyshev, “Correlation functions of the XX Heisenberg magnet and random walks of vicious walkers”, TMF, 159:2 (2009), 179–193; Theoret. and Math. Phys., 159:2 (2009), 563–574
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6341
  • https://doi.org/10.4213/tmf6341
  • https://www.mathnet.ru/eng/tmf/v159/i2/p179
    • This publication is cited in the following 10 articles:
    1. 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  mathnet
    2. 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  crossref
    3. J. Math. Sci. (N. Y.), 242:5 (2019), 628–635  mathnet  crossref
    4. J. Math. Sci. (N. Y.), 238:6 (2019), 779–792  mathnet  crossref
    5. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. J. Math. Sci. (N. Y.), 216:1 (2016), 8–22  mathnet  crossref  mathscinet
    7. J. Math. Sci. (N. Y.), 200:6 (2014), 662–670  mathnet  crossref
    8. Bogoliubov N.M., Malyshev C., “Correlation Functions of Xxo Heisenberg Chain, Q-Binomial Determinants, and Random Walks”, Nucl. Phys. B, 879 (2014), 268–291  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, Theoret. and Math. Phys., 169:2 (2011), 1517–1529  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    10. N. M. Bogoliubov, K. Malyshev, “The correlation functions of the $XXZ$ Heisenberg chain in the case of zero or infinite anisotropy, and random walks of vicious walkers”, St. Petersburg Math. J., 22:3 (2011), 359–377  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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