%0 Journal Article %T On phase transition in the hard-core model on ${\bf Z}^d$ %A David Galvin %A Jeff Kahn %J Mathematics %D 2012 %I arXiv %X It is shown that the hard-core model on ${\bf Z}^d$ exhibits a phase transition at activities above some function $\lambda(d)$ which tends to zero as $d\rightarrow \infty$ %U http://arxiv.org/abs/1206.3144v1