Ola Bratteli & Derek William Robinson 
Operator Algebras and Quantum Statistical Mechanics 
Equilibrium States. Models in Quantum Statistical Mechanics

For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems.Major changes in the new edition relate to Bose–Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented.