Long range order for threedimensional 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 BricmontKupiainen (1988) from the very low temperature regime to the entire low temperature regime.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.13998
 arXiv:
 arXiv:2209.13998
 Bibcode:
 2022arXiv220913998D
 Keywords:

 Mathematics  Probability;
 60K35;
 82B44
 EPrint:
 36 pages