### Abstract

Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For such systems, it is proven that in d=2 dimensions there can be no first-order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter. Discontinuities which would amount to a continuous symmetry breaking, in systems which are (stochastically) invariant under the action of a continuous subgroup of O(N), are suppressed by the randomness in dimensions d≦4. Specific implications are found in the Random-Field Ising Model, for which we conclude that in d=2 dimensions at all (β, h) the Gibbs state is unique for almost all field configurations, and in the Random-Bond Potts Model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point. The results are explained by the argument of Imry and Ma [1]. The proofs involve the analysis of fluctuations of free energy differences, which are shown (using martingale techniques) to be Gaussian on the suitable scale.

Original language | English (US) |
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Pages (from-to) | 489-528 |

Number of pages | 40 |

Journal | Communications In Mathematical Physics |

Volume | 130 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 1990 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*130*(3), 489-528. https://doi.org/10.1007/BF02096933