### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**A Note on Exponential Decay in the Random Field Ising Model.** / Camia, Federico; Jiang, Jianping; Newman, Charles.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 173, no. 2, pp. 268-284. https://doi.org/10.1007/s10955-018-2140-8

}

TY - JOUR

T1 - A Note on Exponential Decay in the Random Field Ising Model

AU - Camia, Federico

AU - Jiang, Jianping

AU - Newman, Charles

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - Coupling

KW - Exponential decay

KW - Kertész line

KW - Random cluster model

KW - Random field Ising model

UR - http://www.scopus.com/inward/record.url?scp=85053251353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053251353&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2140-8

DO - 10.1007/s10955-018-2140-8

M3 - Article

AN - SCOPUS:85053251353

VL - 173

SP - 268

EP - 284

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -