You can specify the line width. Here is a zoomed in view of the output so that one can see the difference:
As John Kormylo pointed out the tikz-pgf manual says about the "0 width" line:
Line width: The “thickness” of the line. A width of 0 is the thinnest width renderable on the device. On a high-resolution printer this may become invisible and should be avoided. A good choice is 0.4pt, which is the default.
Obviously at some point the size difference won't be noticeable at all, especially in a print edition.