S. A. Pirogov, “States associated with the two-dimensional Ising model”, TMF, 11:3 (1972), 421–426; Theoret. and Math. Phys., 11:3 (1972), 614

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Teoreticheskaya i Matematicheskaya Fizika, 1972, Volume 11, Number 3, Pages 421–426 (Mi tmf2881)

This article is cited in 10 scientific papers (total in 10 papers)

States associated with the two-dimensional Ising model

S. A. Pirogov

Full-text PDF (567 kB) Citations (10)

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Abstract: A study is made of states on the algebra of 0uasilocal observables generated by the transfer matrix of the two-dimensional Ising model and its highest eigenvecto r in the infinite-volume limit. Both states are quasifree and the latter (“ground state”) is pure. The limit transfer matrix $P_{\infty}$ is also calculated in the space of the representation associated with the ground state. All the calculations are made by the Onsager–Kaufman method.

Received: 07.09.1971

English version:
Theoretical and Mathematical Physics, 1972, Volume 11, Issue 3, Pages 614–617
DOI: https://doi.org/10.1007/BF01028379

Bibliographic databases:

Language: Russian

Citation: S. A. Pirogov, “States associated with the two-dimensional Ising model”, TMF, 11:3 (1972), 421–426; Theoret. and Math. Phys., 11:3 (1972), 614–617

Citation in format AMSBIB

\Bibitem{Pir72}

\by S.~A.~Pirogov

\paper States associated with the two-dimensional Ising model

\jour TMF

\yr 1972

\vol 11

\issue 3

\pages 421--426

\mathnet{http://mi.mathnet.ru/tmf2881}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=475445}

\transl

\jour Theoret. and Math. Phys.

\yr 1972

\vol 11

\issue 3

\pages 614--617

\crossref{https://doi.org/10.1007/BF01028379}

Linking options:

https://www.mathnet.ru/eng/tmf2881

https://www.mathnet.ru/eng/tmf/v11/i3/p421

This publication is cited in the following 10 articles:

David E. Evans, Yasuyuki Kawahigashi, Quantum and Non-Commutative Analysis, 1993, 341
Alain Connes, David E. Evans, “Embeddings ofU(1)-current algebras in non-commutative algebras of classical statistical mechanics”, Commun.Math. Phys., 121:3 (1989), 507
R. Kuik, “Markov and stability properties of equilibrium states for nearest-neighbor interactions”, Commun.Math. Phys., 115:4 (1988), 529
D. E. Evans, J. T. Lewis, “On aC*-algebra approach to phase transition in the two-dimensional Ising model. II”, Commun.Math. Phys., 102:4 (1986), 521
David E. Evans, Lecture Notes in Mathematics, 1136, Quantum Probability and Applications II, 1985, 162
D. E. Evans, J. T. Lewis, “The spectrum of the transfer matrix in theC*-algebra of the Ising model at high temperatures”, Commun.Math. Phys., 92:3 (1984), 309
Huzihiro Araki, David E. Evans, “On aC*-algebra approach to phase transition in the two-dimensional Ising model”, Commun.Math. Phys., 91:4 (1983), 489
A. P. Bakalkin, Ya. Z. Shapiro, V. P. Rakina, A. N. Gaodu, “A review of the state standard for lightweight refractory products”, Refractories, 20:7-8 (1979), 506
J. T. Lewis, P. N. M. Sisson, “AC*-algebra of the two-dimensional Ising model”, Commun.Math. Phys., 44:3 (1975), 279
J.T. Lewis, P.N.M. Sisson, “A Fermi algebra for the Ising model on an infinite lattice”, Physics Letters A, 50:3 (1974), 197

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	336
Full-text PDF :	111
References:	58
First page:	1

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