## Statistical Mechanics: Rigorous ResultsThis classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century. |

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### Contents

Thermodynamic Behavior Ensembles l | 1 |

The Thermodynamic Limit | 13 |

Some Inequalities for Quantum Systems | 25 |

The Thermodynamic Limit | 29 |

Thermodynamic Limit for the Quantum Ensembles | 60 |

Low Density Expansions | 71 |

Positive Potentials | 93 |

The Problem of Phase Transitions | 108 |

The Theorem ofMermin and Wagner | 129 |

Group Invariance of Physical States | 145 |

Pure Thermodynamic Phases as Ergodic States | 161 |

The Gibbs Phase Rule | 190 |

Von Neumann Algebras | 205 |

### Common terms and phrases

Abelian assume B*-algebra Banach space Chapter classical lattice systems classical systems cluster property compact concludes the proof condition configurations continuous function convergence convex convex function correlation functions corresponding defined dense density matrices eigenvalues entropy equations equilibrium ergodic exists fermions finite range Fisher Friedrichs extension G-invariant grand canonical ensemble grand partition function Hamiltonian hard core Hilbert space Hove identity implies inequality infinite system infinite volume infinity integral isomorphism Lanford lattice gas Lebesgue measurable linear M-net Math matrix microcanonical Microcanonical Ensemble Neumann algebra norm notation obtain pair interaction pair potential particles partition function phase transition Phys physical potential energy Proposition prove quantum lattice systems quantum systems representation restriction Robinson Ruelle satisfied Section self-adjoint operator spin system statistical mechanics subspace temperedness Theorem theory thermodynamic functions thermodynamic limit translation unique vector write yields zero