no. 3
Entropy estimates for finitely correlated states
Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 259-277. 
@article{AIHPA_1992__57_3_259_0,
     author = {Fannes, M. and Nachtergaele, B. and Werner, R. F.},
     title = {Entropy estimates for finitely correlated states},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {259--277},
     publisher = {Gauthier-Villars},
     volume = {57},
     number = {3},
     year = {1992},
     mrnumber = {1185335},
     zbl = {0821.46087},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__57_3_259_0/}
}
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Fannes, M.; Nachtergaele, B.; Werner, R. F. Entropy estimates for finitely correlated states. Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 259-277. http://www.numdam.org/item/AIHPA_1992__57_3_259_0/

[1] L. Accardi and A. Frigerio, Markovian Cocycles, Proc. R. Ir. Acad., Vol. 83A, (2), 1983, pp.251-263. | MR | Zbl

[2] M. Aizenman and E.H. Lieb, The third law of thermodynamics and the degeneracy of the ground state for lattice systems, J. Stat. Phys., Vol. 24, 1981, pp. 279-297. | MR

[3] I. Affleck and E.H. Lieb, A proof of part of Haldane's conjecture on quantum spin chains, Lett. Math. Phys., Vol. 12, 1986, pp. 57-69. | MR

[4] I. Affleck, T. Kennedy, E.H. Lieb and H. Tasaki, Valence bond ground states in isotropic quantum antiferromagnets, Commun. Math. Phys., Vol. 115, 1988, pp. 477-528. | MR

[5] O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics, 2 volumes, Springer Verlag, Berlin, Heidelberg. New York 1979 and 1981. | MR

[6] M. Fannes, B. Nachtergaele and R.F. Werner, Finitely correlated states of quantum spin chains, Commun. Math. Phys., Vol. 144, 1992, pp. 443-490. | MR | Zbl

[7] M. Fannes, B. Nachtergaele and R.F. Werner, Valence bond states on quantum spin chains as ground states with spectral gap, J. Phys. A, Vol. 24, 1991, pp. L185- L190. | MR

[8] P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica, Vol. 9D, 1983, pp.189-205. | MR | Zbl

[9] P. Grassberger and I. Procaccia, Dimensions and entropies of strange attractors from a fluctuating dynamics point of view, Physica, Vol. 13D, 1984, pp. 34-54. | MR | Zbl

[10] F.D.M. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: identification with the O (3) nonlinear sigma model, Phys. Lett., Vol. 93A, 1983, pp. 464-468. | MR

[11] T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia and B.I. Shraiman, Fractal measures and their singularities: the characterization of strange sets, Phys. Rev., Vol. 33A, 1986, pp. 1141-1151. | MR

[12] H.G.E. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica, Vol. 8D, 1983, pp.435-444. | MR | Zbl

[13] L. Van Hove, Quelques propriétés générales de l'intégrale de configuration d'un système de particules avec interaction, Physica, Vol. 15, 1949, pp. 951-961. | Zbl

[14] M.G. Kreĭn and M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Transl. Am. Math. Soc. Series 1, Vol. 10, 1966, pp. 199-325.

[15] B. Nachtergaele and L. Slegers, The ground state and its entropy for a class of one dimensional classical lattice systems, Physica, Vol. 149A, 1988, pp. 432-446. | MR

[16] S. Redner, One-dimensional Ising chain with competing interactions: exact results and connection with other statistical models, J. Stat. Phys., Vol. 25, 1981, pp. 15-23. | MR

[17] A. Rényi, On measures of entropy and information, Proc. 4th Berkeley Symp. Math. Statist. Prob., 1960, University of California Press Berkeley, 1961. | MR | Zbl

[18] H.H. Schaefer, Topological vector spaces, Springer-Verlag, New York, Heidelberg, Berlin, 1971. | MR | Zbl

[19] L. Slegers, The residual entropy for a class of one-dimensional lattice models, J. Phys., Vol. 21A, 1988, pp. 3489-3500. | MR

[20] W.F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc., Vol. 6, 1955, pp.211-216. | MR | Zbl

[21] E. Størmer, Positive maps of C*-algebras, in A. HARTKÄMPER, and H. NEUMANN Eds., Foundations of quantum mechanics and ordered linear spaces, Lecture Notes in Physics 29, Springer Verlag, Berlin, Heidelberg, New York, 1974.

[22] G. Toulouse, Theory of the frustration effect in spin glasses: I, Commun. Phys., Vol. 2, 1977, pp. 115-119.