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Baraviera, L. M. Cioletti, A. O. Lopes, J. Mohr and R. R. Souza. Denote the Gibbs measure by $\\mu_{c}:=h_{c}\\nu_{c}$, where $h_{c}$ is the eigenfunction, and, $\\nu_{c}$ is the eigenmeasure of the Ruelle operator associated to $cf$. We are going to prove that any measure selected by $\\mu_{c}$, as $c\\to +\\infty$, is a maximizing measure for $f$. 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Lopes, Jairo Mengue","submitted_at":"2011-06-15T23:14:02Z","abstract_excerpt":"We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\\mathbb{N}}$. The shift acting on $X$ is denoted by $\\sigma$.\n  We analyze the general XY model, as presented in a recent paper by A. T. Baraviera, L. M. Cioletti, A. O. Lopes, J. Mohr and R. R. Souza. Denote the Gibbs measure by $\\mu_{c}:=h_{c}\\nu_{c}$, where $h_{c}$ is the eigenfunction, and, $\\nu_{c}$ is the eigenmeasure of the Ruelle operator associated to $cf$. We are going to prove that any measure selected by $\\mu_{c}$, as $c\\to +\\infty$, is a maximizing measure for $f$. 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