KMS states and branched points

Masaki Izumi, Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We completely classify the Kubo-Martin-Schwinger (KMS) states for the gauge action on a C*-algebra associated with a rational function R introduced in our previous work. The gauge action has a phase transition at β = log deg R. We can recover the degree of R, the number of branched points, the number of exceptional points and the orbits of exceptional points from the structure of the KMS states. We also classify the KMS states for C*-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method.

Original languageEnglish
Pages (from-to)1887-1918
Number of pages32
JournalErgodic Theory and Dynamical Systems
Volume27
Issue number6
DOIs
Publication statusPublished - Dec 1 2007

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Algebra
Gages
C*-algebra
Rational functions
Gauge
Classify
Tent Map
Self-similar Set
Sierpinski Gasket
Orbits
Phase transitions
Rational function
Phase Transition
Orbit

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

KMS states and branched points. / Izumi, Masaki; Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Ergodic Theory and Dynamical Systems, Vol. 27, No. 6, 01.12.2007, p. 1887-1918.

Research output: Contribution to journalArticle

Izumi, M, Kajiwara, T & Watatani, Y 2007, 'KMS states and branched points', Ergodic Theory and Dynamical Systems, vol. 27, no. 6, pp. 1887-1918. https://doi.org/10.1017/S014338570700020X
Izumi, Masaki ; Kajiwara, Tsuyoshi ; Watatani, Yasuo. / KMS states and branched points. In: Ergodic Theory and Dynamical Systems. 2007 ; Vol. 27, No. 6. pp. 1887-1918.
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