RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2009, Volume 159, Number 2, Pages 179–193 (Mi tmf6341)  

This article is cited in 8 scientific papers (total in 8 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

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

DOI: https://doi.org/10.4213/tmf6341

Full text: PDF file (499 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2009, 159:2, 563–574

Bibliographic databases:


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
\Bibitem{BogMal09}
\by N.~M.~Bogolyubov, K.~L.~Malyshev
\paper Correlation functions of the~XX Heisenberg magnet and random walks of vicious walkers
\jour TMF
\yr 2009
\vol 159
\issue 2
\pages 179--193
\mathnet{http://mi.mathnet.ru/tmf6341}
\crossref{https://doi.org/10.4213/tmf6341}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2567335}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...159..563B}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 159
\issue 2
\pages 563--574
\crossref{https://doi.org/10.1007/s11232-009-0046-y}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000269080500001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350012136}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6341
  • https://doi.org/10.4213/tmf6341
  • http://mi.mathnet.ru/eng/tmf/v159/i2/p179

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    2. 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
    3. J. Math. Sci. (N. Y.), 200:6 (2014), 662–670  mathnet  crossref
    4. 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
    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.), 238:6 (2019), 779–792  mathnet  crossref
    8. J. Math. Sci. (N. Y.), 242:5 (2019), 628–635  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:404
    Full text:147
    References:51
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020