Phase transitions in low-dimensional long-range random field Ising models

Jian Ding, Fenglin Huang, João Maia

We consider the long-range random field Ising model in dimension $d=1,2$, whereas the long-range interaction is of the form $J_{xy}=|x-y{|}^{-\hat{I}\pm }$ with $1<\hat{I}\pm <3/2$ for $d=1$ an…