Communications in Mathematical Physics

, Volume 217, Issue 3, pp 555–577 | Cite as

Phase Transitions for Countable Markov Shifts

  • Omri M. Sarig


We study the analyticity of the topological pressure for some one-parameter families of potentials on countable Markov shifts. We relate the non-analyticity of the pressure to changes in the recurrence properties of the system. We give sufficient conditions for such changes to exist and not to exist. We apply these results to the Manneville–Pomeau map, and use them to construct examples with different critical behavior.


Phase Transition Critical Behavior Markov Shift Topological Pressure Recurrence Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Omri M. Sarig
    • 1
  1. 1.Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK.¶E-mail:

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