Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.10318 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915022147420160 |
|---|---|
| author | Prodromidis, Kyprianos-Iason Sly, Allan |
| author_facet | Prodromidis, Kyprianos-Iason Sly, Allan |
| contents | In this note, we prove that on any graph of maximal degree $d$ the mixing time of the Glauber Dynamics for the Ising Model at $β_c=\tanh^{-1}(\frac1{d-1})$, the uniqueness threshold on the infinite $d$-regular tree, is at most polynomial in $n$. The proof follows by a simple combination of new log-Sobolev bounds of Bauerschmidt and Dagallier, together with the tree of self avoiding walks construction of Weitz. While preparing this note we became aware that Chen, Chen, Yin and Zhang recently posted another proof of this result. We believe the simplicity of our argument is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial Mixing of the critical Glauber Dynamics for the Ising Model Prodromidis, Kyprianos-Iason Sly, Allan Probability In this note, we prove that on any graph of maximal degree $d$ the mixing time of the Glauber Dynamics for the Ising Model at $β_c=\tanh^{-1}(\frac1{d-1})$, the uniqueness threshold on the infinite $d$-regular tree, is at most polynomial in $n$. The proof follows by a simple combination of new log-Sobolev bounds of Bauerschmidt and Dagallier, together with the tree of self avoiding walks construction of Weitz. While preparing this note we became aware that Chen, Chen, Yin and Zhang recently posted another proof of this result. We believe the simplicity of our argument is of independent interest. |
| title | Polynomial Mixing of the critical Glauber Dynamics for the Ising Model |
| topic | Probability |
| url | https://arxiv.org/abs/2411.10318 |