Large deviations for quantum spin systems

Details Large deviations for quantum spin systems Large deviations for quantum spin systems

2004-04-06

arxiv.org/abs/math-ph/0404018v1

J. Stat. Phys. 117:521-547 (2004)

Physics

Mathematical Physics

22 pages

Scientific paper

10.1007/s10955-004-3452-4

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 $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'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 $\frac{1}{|\Lambda|}\sum_{i\in\Lambda} \delta_{X_i}$.

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