Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type

Journal of Statistical Physics

Volumn 119, Issue 3-4, 2005, Pages 765-776

  Jenkinson, O ^a   Mauldin, R D ^b   Urbanski M ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

Countable alphabet subshift of finite type; Equilibrium state; Gibbs state; Ground state; Maximizing measure

Indexed keywords

EID: 21644444145     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-3035-z     Document Type: Article

References (21)

1. M. Aizenman and E. H. Lieb, The third law of thermodynamics and the degeneracy of the ground state for lattice systems, J. Stat. Phys. 24:279-297 (1981).
2. P. Billingsley, Convergence of Probability Measures (John Wiley & Sons, New York, 1968).
3. R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer Lecture Notes in Mathematics Vol. 470 (Berlin-Heidelberg-New York, Springer-Verlag, 1975).
4. J. Brémont, On the behaviour of Gibbs measures at temperature zero, Nonlinearity 16:419-426 (2003).
5. J. Buzzi and O. Sarig, Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps, Ergod. Th. Dyn. Syst. 23:1383-1400 (2003).
6. Z. N. Coelho, Entropy and ergodicity of skew-products over subshifts of finite type and central limit asymptotics, Ph.D. Thesis (Warwick University, 1990).
7. G. Contreras, A. O. Lopes, and Ph. Thieullen, Lyapunov minimizing measures for expanding maps of the circle, Ergod. Th. Dyn. Syst. 21:1379-1409 (2001).
8. J.-P. Conze and Y. Guivarc'h, Croissance des sommes ergodiques, manuscript, circa (1993).
9. O. Jenkinson, Geometric barycentres of invariant measures for circle maps, Ergod. Th. Dyn. Syst. 21:511-532 (2001).
10. O. Jenkinson, R. D. Mauldin and M. Urbariski, Ergodic optimization for countable state subshifts of finite type, preprint.
11. A. Kerimov, Countable extreme Gibbs states in a one-dimensional model with unique ground state, J. Phys. A: Math. Gen. 31:2815-2821 (1998).
12. R. D. Mauldin and M. Urbahski, Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets (Cambridge University Press, 2003).
13. q extensions of subshifts of finite type, J. London Math. Soc. 49:401-416 (1994).
14. C. Radin, Ordering in lattice gases at low temperature, J. Phys. A 22:317-319 (1989).
15. C. Radin, Disordered ground states of classical lattice models, Rev. Math. Phys. 3:125-135 (1991).
16. n versus Z actions for systems of finite type, Symbolic dynamics and its applications (New Haven, CT, 1991), 339-342, Contemp. Math., 135, Amer. Math. Soc., Providence, RI, 1992.
17. D. Ruelle, Thermodynamic Formalism, Encyclopaedia of Mathematics and its Applications, Vol. 5 (Addison-Wesley, 1978).
18. O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergod. Th. Dyn. Syst. 19:1565-1593 (1999).
19. O. Sarig, Characterization of existence of Gibbs measures for countable Markov shifts, Proc. Am. Math. Soc. 131:1751-1758 (2003).
20. R. Schrader, Ground states in classical lattice systems with hard core, Comm. Math. Phys. 16:247-264 (1970).
21. P. Walters, An Introduction to Ergodic Theory (Springer, 1981).