摘 要：In this talk, we give some basic comcepts and results on the general theory of equilibrium statistical mechanics of classical lattice systems, which are from Ruelle’s classical monograph “Thermodynamic Formalism: The Mathematical Structures of Equilibrium Statistical Mechanics”. Firstly, we give the theory of Gibbs states, without assuming invariance under lattice translations. Then, assuming translation invariance we introduce the theory of equilibrium states and of the pressure for classical lattice systems; general results on phase transitions are also given. We also discuss the connection between Gibbs states and equilibrium states. In the last, we talk about one-dimensional systems and some recent advance on this topic.
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