I've just learned something. There are at least two railroad tracks named the Peavine. Bobert says there's one in Mississippi. The other is in Arizona. Here's info from a blog which gives you the dope on that one:
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The Peavine & Santa Fe Model Railroad

The Peavine & Santa Fe is a model Railroad inspired by the real Santa Fe branchline in Arizona from Ash Fork on the Santa Fe mainline to Phoenix. The original name of this line was "The Santa Fe, Prescott & Phoenix Railway".

Both lines are called the Peavine because they have an unusual number of curves and twists.