  Arboreal Gas is a type of (unrooted) random forest on a graph, where the
probability is determined by a parameter $\beta>0$ per edge. This model is
essentially equivalent to acyclic Bernoulli bond percolation with a parameter
$p=\beta/(1+\beta)$. Additionally, Arboreal Gas can be considered as the limit
of the $q$-states random cluster model with $p=\beta q$ as $q\to 0$. A natural
question arises regarding the existence and performance of the weak limit of
Arboreal Gas as the graph size goes to infinity. The answer to this question
relies on the negative correlation of Arboreal Gas, which is still an open
problem. This paper primarily focuses on the negative correlation of Arboreal
Gas and provides some results for specific graphs.
