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- W1900229606 abstract "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 $sigma$. 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 $cto +infty$, is a maximizing measure for $f$. We also show, when the maximizing probability measure is unique, that it is true a Large Deviation Principle, with the deviation function $R_{+}^{infty}=sum_{j=0}^infty R_{+} (sigma^f)$, where $R_{+}:= beta(f) + Vcircsigma - V - f$, and, $V$ is any calibrated subaction." @default.
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- W1900229606 date "2011-06-15" @default.
- W1900229606 modified "2023-09-27" @default.
- W1900229606 title "Selection of measure and a Large Deviation Principle for the general XY model" @default.
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