## Abstract

I use Israel's methods to prove new theorems of "ubiquitous pathology" for classical and quantum lattice systems. The main result is the following: Let Φ be any interaction and ρ{variant} be any translation-invariant equilibrium state for Φ (extremal or not). Then there exists a sequence {Φ_{k}} of interactions converging to Φ, having extremal (or even unique) translation-invariant equilibrium states ρ{variant}_{k}, such that {ρ{variant}_{k}} converges to ρ{variant}. In certain situations the perturbations Φ_{k}-Φ can be chosen to lie in a cone of "antiferromagnetic pair interactions." I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r^{2} interaction (Thouless effect).

Original language | English (US) |
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Pages (from-to) | 327-336 |

Number of pages | 10 |

Journal | Communications In Mathematical Physics |

Volume | 86 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1982 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics