### Abstract

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.

Original language | English (US) |
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Pages (from-to) | 268-284 |

Number of pages | 17 |

Journal | Journal of Statistical Physics |

Volume | 173 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2018 |

### Keywords

- Coupling
- Exponential decay
- Kertész line
- Random cluster model
- Random field Ising model

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*173*(2), 268-284. https://doi.org/10.1007/s10955-018-2140-8