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
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
supk∑l≠kexp{−βε(k,l)}≤ˉψ1, where ˉψ1
is a small number. The pressure in the ensemble is p(ˆz)=supk∈Φbk(ˆz)=|ˆb(ˆz)|. The
limit Gibbs states corresponding to the vector ˆz are small
perturbations of the ground states α(x)=q∈G1(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 zl∂p/∂zl are continuous in the closure of a region of
constancy of G1(ˆz).
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
\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}
Linking options:
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This publication is cited in the following 11 articles: