### Abstract

We study certain quantum spin systems which are equivalent to stochastic Ising models. We show that any translationally invariant quantum ground state is given by integration of Gibbs measure. The existence of mass gap is shown to be the same as exponentially fast convergence of stochastic models to invariant states.

Original language | English |
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Pages (from-to) | 79-89 |

Number of pages | 11 |

Journal | Communications in Mathematical Physics |

Volume | 135 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 1990 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics