Preventing Neighbor's Ivy from Growing Under Fence?

I put a vegetable box in the back yard along the fence, but little did i know that my neighbor has an ivy. Since I've put in the box, the ivy has been creeping over from underneath, which makes any kind of garden impossible. The only solution that I've thought of was to put some kind of plastic cover on the bottom of the box to try to prevent the ivy from coming over. Would that work? If not any suggestions?