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biblio.tex
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biblio.tex
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\begin{thebibliography}{999}
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Discontinuity of the magnetization in the one-dimensional $1/|x-y|^2$ Ising
and Potts models, {\em J.\ Statist.\ Phys.\ } {\bf 50} (1988), 1--40.
\bibitem{berger} N.\ Berger, C.\ Hoffman and V.\ Sidoravicius, Nonuniqueness for
specifications in $\ell^{2+\epsilon}$, to appear (2017) in {\em Ergodic Theory
Dynam.\ Systems}.
\bibitem{berbee1} H. Berbee, Chains with Infinite Connections: Uniqueness and
Markov Representation, {\em Probab.\ Theory Related Fields} {\bf 76} (1987),
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\bibitem{berbee2} H. Berbee, Uniqueness of Gibbs measures and absorption
probabilities, {\em Ann.\ Probab.\ } {\bf 17} (1989), no.\ 4, 1416--1431.
\bibitem{lop1} L.\ Cioletti and A.\ Lopes, Interactions, Specifications, DLR
probabilities and the Ruelle Operator in the One-Dimensional Lattice,
preprint, arXiv:1404.3232.
\bibitem{lop3} L.\ Cioletti and A.\ Lopes, Ruelle Operator for Continuous
Potentials and DLR-Gibbs Measures, preprint, arXiv:1608.03881v1.
\bibitem{FS} J.\ Fr\"olich and T.\ Spencer, The phase transition in the
one-dimensional Ising Model with $1/r^2$ interaction energy, {\em Comm.\
Math.\ Phys.\ } {\bf 4} (1982), no.\ 1, 87--101.
\bibitem{johob} A.\ Johansson and A.\ \"Oberg, Square summability of variations
of $g$-functions and uniqueness of $g$-measures, {\em Math.\ Res.\ Lett.\ }
{\bf 10} (2003), no.\ 5--6, 587--601.
\bibitem{jop1} A.\ Johansson, A.\ \"Oberg and M.\ Pollicott, Countable state
shifts and uniqueness of $g$-measures, {\em Amer.\ J.\ Math.\ } {\bf 129}
(2007), 1501--1511.
\bibitem{jop2} A.\ Johansson, A.\ \"Oberg and M.\ Pollicott, Unique Bernoulli
$g$-measures, {\em J.\ Eur.\ Math.\ Soc.\ } {\bf 14} (2012), 1599--1615.
\bibitem{jop3} A.\ Johansson, A.\ \"Oberg and M.\ Pollicott, Phase transitions
in long-range Ising models and an optimal condition for factors of
$g$-measures, {\em Ergodic Theory \& Dynam.\ Systems} {\bf 39} (2019,
1317--1330.
\bibitem{keane} M.\ Keane, Strongly mixing $g$-measures, {\em Invent.\ Math.\ }
{\bf 16} (1972), 309--324.
\bibitem{kesten} M.\ Aizenman, H.\ Kesten and C.M.\ Newman, Uniqueness of the
Infinite Cluster and Continuity of Connectivity Functions for Short and Long
Range Percolation, {\em Commun.\ Math.\ Phys.\ } {\bf 111} (1987), 505--531.
\bibitem{sin} Ya.G.\ Sinai, Gibbs measures in ergodic theory, {\em Russian
Mathematical Surveys} {\bf 27}(4) (1972), 21--69.
\bibitem{walters1} P.\ Walters, Ruelle's operator theorem and $g$-measures, {\em
Trans.\ Amer.\ Math.\ Soc.\ } {\bf 214} (1975), 375--387.
\bibitem{walters3} P.\ Walters, Convergence of the Ruelle Operator, {\em Trans.\
Amer.\ Math.\ Soc.\ } {\bf 353} (2000), no.\ 1, 327--347.
\end{thebibliography}
\noindent
\newline
\noindent
Anders Johansson, Department of Mathematics, University of G\"avle, 801 76
G\"avle, Sweden. Email-address: ajj@hig.se\newline
\noindent
Anders \"Oberg, Department of Mathematics, Uppsala University, P.O.\ Box 480,
751 06 Uppsala, Sweden. E-mail-address: anders@math.uu.se\newline