Long range order for three-dimensional random field Ising model throughout the entire low temperature regime
Abstract
For $d\geq 3$, we study the Ising model on $\mathbb Z^d$ with random field given by $\{\epsilon h_v: v\in \mathbb Z^d\}$ where $h_v$'s are independent normal variables with mean 0 and variance 1. We show that for any $T < T_c$ (here $T_c$ is the critical temperature without disorder), long range order exists as long as $\epsilon$ is sufficiently small depending on $T$. Our work extends previous results of Imbrie (1985) and Bricmont--Kupiainen (1988) from the very low temperature regime to the entire low temperature regime.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- 10.48550/arXiv.2209.13998
- arXiv:
- arXiv:2209.13998
- Bibcode:
- 2022arXiv220913998D
- Keywords:
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- Mathematics - Probability;
- 60K35;
- 82B44
- E-Print:
- 36 pages