Large Deviations for Quantum Spin Systems

Author： Netočný K.   Redig F.  

Publisher： Springer Publishing Company

ISSN： 0022-4715

Source： Journal of Statistical Physics, Vol.117, Iss.3-4, 2004-11, pp. : 521-546

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Abstract

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages \overline{X}_{\varLambda} :=\frac{1}{|\varLambda|} \sum_{i\in\varLambda} X_i, where the Xi’s are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of \frac{1}{|\la|}\sum_{i\in\la} \delta_{X_i}

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