Which areas of computer science have lots of overlap with physics?
[The following is more an extended comment with pointers than a real answer.]

If you were in France, a good answer would be combinatorial physics.  I say "if you were in France" because, for reasons that escape me but that must be mostly historical, in France combinatorics is considered part of theoretical computer science :-)  In the rest of the world, combinatorics is considered to be a branch of mathematics, so I guess it is more correct to say that combinatorial physics is about interactions between physics and discrete math, rather than CS.

Anyway, in my lab (which is a CS lab) there's a research group which focuses on several aspects of combinatorics, in particular combinatorial physics.  This is by no means the only example in France of a combinatorics group in a CS lab whose research overlaps with physics; another example off the top of my head is this one in Bordeaux. Some of the members of these groups are theoretical physicists.

The "official" recognition of combinatorial physics as a research field of its own is very recent, as you may read in this blog post, which contains some pointers and basic info about it.  Computer science is explicitly mentioned a couple of times, although maybe not exactly in the sense you would expect, but I am sure that my colleagues from those research group would be able to give you more precise answers.  Maybe you can start checking out their web pages for additional info.