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 |
|---|---|
| Pages (from-to) | 268-284 |
| Number of pages | 17 |
| Journal | Journal of Statistical Physics |
| Volume | 173 |
| Issue number | 2 |
| Early online date | 30 Aug 2018 |
| DOIs | |
| Publication status | Published - Oct 2018 |
Funding
Acknowledgements The research of JJ was partially supported by STCSM Grant 17YF1413300 and that of CMN by US-NSF Grant DMS-1507019. The authors thank Dan Stein and Janek Wehr for useful discussions. They also thank the Institute of Applied Mathematics of the Chinese Academy of Sciences, where some of the work reported here was done.
| Funders | Funder number |
|---|---|
| US-NSF | DMS-1507019 |
| Science and Technology Commission of Shanghai Municipality | 17YF1413300 |
Keywords
- Coupling
- Exponential decay
- Kertész line
- Random cluster model
- Random field Ising model
