Abstract
The paper presents an example of a one-parameter group of automorphisms on the Cuntz algebra O 2 for which the KMS states exhibit a phase transition. The factor type of the extremal KMS states are determined.
Similar content being viewed by others
References
Anantharaman-Delaroche C.: Purely infinite C*-algebras arising from dynamical systems. Bull. Soc. Math. France 125, 199–225 (1997)
Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics I + II, Texts and Monographs in Physics, Springer Verlag, New York, Heidelberg, Berlin (1979, 1981)
Connes A.: Une classification des facteurs de type III. Ann. Sci. Ecole Norm. Sup. 6, 133–252 (1973)
Cuntz J.: Simple C*-algebras generated by isometries. Commun. Math. Phys. 57, 173–185 (1977)
Deaconu V.: Groupoids associated with endomorphisms. Trans. Am. Math. Soc. 347, 1779–1786 (1995)
Denker M., Urbanski M.: On the existence of conformal measures. Trans. Am. Math. Soc. 328, 563–587 (1991)
Exel R.: KMS states for generalized gauge actions on Cuntz-Krieger algebras (an application of the Ruelle-Perron-Frobenius theorem). Bull. Braz. Math. Soc. (N.S) 35, 1–12 (2004)
Haagerup U.: Connes’ bicentralizer problem and uniqueness of the injective factor of type III 1. Acta Math. 158, 95–148 (1987)
Hofbauer F.: Examples for the non-uniqueness of the equilibrium state. Trans. Am. Math. Soc. 228, 223–241 (1977)
Kadison R.V., Ringrose J.R.: Fundamentals of the Theory of Operator Algebras II. Academic, London (1986)
Neshveyev S.: KMS states on the C*-algebras of non-principal groupoids. J. Oper. Theory 70, 513–530 (2013)
Olesen D., Pedersen G.K.: Some C*-dynamical systems with a single KMS-state. Math. Scand. 42, 111–118 (1978)
Pedersen G.K.: C*-Algebras and their automorphism groups. Academic, London (1979)
Renault J.: A Groupoid Approach to C*-algebras, LNM 793. Springer Verlag, Berlin, Heidelberg, New York (1980)
Renault, J.: Cuntz-like algebras, Operator theoretical methods (Timisoara, 1998), pp. 371–386, Theta Found., Bucharest (2000)
Thomsen, K.: KMS-and conformal measures. Commun. Math. Phys. 316, 615–640 (2012) doi:10.1007/s00220-012-1591-z
Thomsen K.: KMS weights on groupoid and graph C*-algebras. J. Funct. Anal. 266, 2959–2988 (2014)
Thomsen, K.: KMS weights on graph C*-algebras II. Factor types and ground states. arXiv:1412.6762
Walters P.: A natural space of functions for the Ruelle operator theorem. Ergod. Theory Dyn. Syst. 27, 1323–1348 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Y. Kawahigashi
I mindet om Uffe Haagerup
Rights and permissions
About this article
Cite this article
Thomsen, K. Phase Transition in O 2 . Commun. Math. Phys. 349, 481–492 (2017). https://doi.org/10.1007/s00220-016-2742-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-016-2742-4