  We prove the existence of global minimizers of Allen-Cahn equation in
dimensions $8$ and above. More precisely, given any strictly area-minimizing
Lawson's cones, there are global minimizers whose nodal sets are asymptotic to
the cones. As a consequence of Jerison-Monneau's program we establish the
existence of many counter-examples to the De Giorgi's conjecture different from
the Bombierie-De Giorgi-Giusti minimal graph.
