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Decrease properties of truncated correlation functions and analyticity properties for classical lattices and continuous systems. (English) Zbl 1125.82302
Summary: We present and discuss some physical hypotheses on the decrease of truncated correlation functions and we show that they imply the analyticity of the thermodynamic limits of the pressure and of all correlation functions with respect to the reciprocal temperature $\beta$ and the magnetic field $h$ (or the chemical potential $mu$) at all (real) points $\left({\beta }_{0},{h}_{0}\right)$ (or $\left({\beta }_{0},{\mu }_{0}\right)$) where they are supposed to hold. A decrease close to our hypotheses is derived in certain particular situations at the end.
##### MSC:
 82B05 Classical equilibrium statistical mechanics (general) 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
##### References:
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