Phase Transitions in Multidimensional Long-Range Random Field Ising Models
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913999793160192 |
|---|---|
| author | Affonso, Lucas Bissacot, Rodrigo Maia, João |
| author_facet | Affonso, Lucas Bissacot, Rodrigo Maia, João |
| contents | We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range interactions and prove the phase transition in a class of ferromagnetic random field Ising models. Our proof combines a generalization of Fröhlich-Spencer contours to the multidimensional setting, proposed by two of us, with the coarse-graining procedure introduced by Fisher, Fröhlich, and Spencer. Our result shows that the Ding-Zhuang strategy is also useful for interactions $J_{xy}=|x-y|^{- α}$ when $α> d$ in dimension $d\geq 3$ if we have a suitable system of contours, yielding an alternative approach that does not use the Renormalization Group Method (RGM), since Bricmont and Kupiainen suggested that the RGM should also work on this generality. We can consider i.i.d. random fields with Gaussian or Bernoulli distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14150 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase Transitions in Multidimensional Long-Range Random Field Ising Models Affonso, Lucas Bissacot, Rodrigo Maia, João Mathematical Physics Statistical Mechanics Probability 82Bxx, 82B44, 82B05, 82B26, 60k35 We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range interactions and prove the phase transition in a class of ferromagnetic random field Ising models. Our proof combines a generalization of Fröhlich-Spencer contours to the multidimensional setting, proposed by two of us, with the coarse-graining procedure introduced by Fisher, Fröhlich, and Spencer. Our result shows that the Ding-Zhuang strategy is also useful for interactions $J_{xy}=|x-y|^{- α}$ when $α> d$ in dimension $d\geq 3$ if we have a suitable system of contours, yielding an alternative approach that does not use the Renormalization Group Method (RGM), since Bricmont and Kupiainen suggested that the RGM should also work on this generality. We can consider i.i.d. random fields with Gaussian or Bernoulli distributions. |
| title | Phase Transitions in Multidimensional Long-Range Random Field Ising Models |
| topic | Mathematical Physics Statistical Mechanics Probability 82Bxx, 82B44, 82B05, 82B26, 60k35 |
| url | https://arxiv.org/abs/2307.14150 |