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Teoreticheskaya i Matematicheskaya Fizika, 1984, Volume 58, Number 2, Pages 261–278 (Mi tmf4526)  

This article is cited in 11 scientific papers (total in 11 papers)

Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states

A. G. Basuev
References:
Abstract: It is shown that at low temperatures and for arbitrary external fields (activities zk, ˆz={zk}) the ensemble with the Hamiltonian (1) and particles in the set Φ is equivalent to |Φ| Ising models with activities bk(ˆz),ˆb(ˆz)={bk(ˆz)}. The mapping ˆb(ˆz) is a homeomorphism on the positive octant l(Φ) if supklkexp{βε(k,l)}ˉψ1, where ˉψ1 is a small number. The pressure in the ensemble is p(ˆz)=supkΦbk(ˆz)=|ˆb(ˆz)|. The limit Gibbs states corresponding to the vector ˆz are small perturbations of the ground states α(x)=qG1(ˆz) and are labeled by elements of the set G1(ˆz)={ˆq:lnbq(ˆz)=p(ˆz)}, where the function G1(ˆz) defines the phase diagram of the ensemble. In the regions of constancy of G1(ˆz) the pressure can be continued to a holomorphie function, and the particle densities zlp/zl are continuous in the closure of a region of constancy of G1(ˆz).
Received: 19.05.1983
English version:
Theoretical and Mathematical Physics, 1984, Volume 58, Issue 2, Pages 171–182
DOI: https://doi.org/10.1007/BF01017924
Bibliographic databases:
Language: Russian
Citation: A. G. Basuev, “Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states”, TMF, 58:2 (1984), 261–278; Theoret. and Math. Phys., 58:2 (1984), 171–182
Citation in format AMSBIB
\Bibitem{Bas84}
\by A.~G.~Basuev
\paper Complete phase diagrams with respect to external fields at low temperatures for models with nearest-neighbor interaction in the case of a finite or countable number of ground states
\jour TMF
\yr 1984
\vol 58
\issue 2
\pages 261--278
\mathnet{http://mi.mathnet.ru/tmf4526}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=743412}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 58
\issue 2
\pages 171--182
\crossref{https://doi.org/10.1007/BF01017924}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984TG27600012}
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  • https://www.mathnet.ru/eng/tmf4526
  • https://www.mathnet.ru/eng/tmf/v58/i2/p261
  • This publication is cited in the following 11 articles:
    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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    References:68
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