The history of Mathematical Physics includes many examples of both of its constituent disciplines providing insight to the other. The mathematical tools of differential equations, linear algebra, and manifolds have allowed for precise descriptions of physical models; at the same time, formulas such as the Riemann-Roch Theorem and the ongoing X=M Conjecture could never have been discovered without deep physical insight.
In this article (which I found by way of Slashdot) we see an example of Physics informing the study of social networks. The authors point out that Physics is, in some sense, just returning the favor Sociology lent it about 100 years ago by inspiring the use of probabilistic models for gases, rather than relying on determinism.
Personally, I want to know if a mechanistic relationship exists between statistical particle models and large groups of people. Sadly, such a connection is missing from the current stage of this research; not surprising, since it is still so new. Once that bridge is built, however, a new paradigm for complex systems will likely emerge. There's no telling what we might be able to do then.