@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},
volume = {56},
year = {1992},
pages = {259-277},
mrnumber = {1185335},
zbl = {0821.46087},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1992__57_3_259_0}
}
Fannes, M.; Nachtergaele, B.; Werner, R. F. Entropy estimates for finitely correlated states. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 259-277. http://gdmltest.u-ga.fr/item/AIHPA_1992__57_3_259_0/
[1] and , Markovian Cocycles, Proc. R. Ir. Acad., Vol. 83A, (2), 1983, pp.251-263. | MR 736500 | Zbl 0534.46045
[2] and , 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 601698
[3] and , A proof of part of Haldane's conjecture on quantum spin chains, Lett. Math. Phys., Vol. 12, 1986, pp. 57-69. | MR 849254
[4] , , and , Valence bond ground states in isotropic quantum antiferromagnets, Commun. Math. Phys., Vol. 115, 1988, pp. 477-528. | MR 931672
[5] and , Operator algebras and quantum statistical mechanics, 2 volumes, Springer Verlag, Berlin, Heidelberg. New York 1979 and 1981. | MR 1441540
[6] , and , Finitely correlated states of quantum spin chains, Commun. Math. Phys., Vol. 144, 1992, pp. 443-490. | MR 1158756 | Zbl 0755.46039
[7] , and , Valence bond states on quantum spin chains as ground states with spectral gap, J. Phys. A, Vol. 24, 1991, pp. L185- L190. | MR 1104168
[8] and , Measuring the strangeness of strange attractors, Physica, Vol. 9D, 1983, pp.189-205. | MR 732572 | Zbl 0593.58024
[9] and , Dimensions and entropies of strange attractors from a fluctuating dynamics point of view, Physica, Vol. 13D, 1984, pp. 34-54. | MR 775277 | Zbl 0587.58031
[10] , 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 697677
[11] , , , and , Fractal measures and their singularities: the characterization of strange sets, Phys. Rev., Vol. 33A, 1986, pp. 1141-1151. | MR 823474
[12] and , The infinite number of generalized dimensions of fractals and strange attractors, Physica, Vol. 8D, 1983, pp.435-444. | MR 719636 | Zbl 0538.58026
[13] , Quelques propriétés générales de l'intégrale de configuration d'un système de particules avec interaction, Physica, Vol. 15, 1949, pp. 951-961. | Zbl 0036.40602
[14] and , Linear operators leaving invariant a cone in a Banach space, Transl. Am. Math. Soc. Series 1, Vol. 10, 1966, pp. 199-325.
[15] and , The ground state and its entropy for a class of one dimensional classical lattice systems, Physica, Vol. 149A, 1988, pp. 432-446. | MR 944036
[16] , 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 610689
[17] , On measures of entropy and information, Proc. 4th Berkeley Symp. Math. Statist. Prob., 1960, University of California Press Berkeley, 1961. | MR 132570 | Zbl 0106.33001
[18] , Topological vector spaces, Springer-Verlag, New York, Heidelberg, Berlin, 1971. | MR 342978 | Zbl 0217.16002
[19] , The residual entropy for a class of one-dimensional lattice models, J. Phys., Vol. 21A, 1988, pp. 3489-3500. | MR 960417
[20] , Positive functions on C*-algebras, Proc. Amer. Math. Soc., Vol. 6, 1955, pp.211-216. | MR 69403 | Zbl 0064.36703
[21] , 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] , Theory of the frustration effect in spin glasses: I, Commun. Phys., Vol. 2, 1977, pp. 115-119.