I have an association with classical Statistical Mechanics. You may check Asano contraction. (I am not a true St.Mech.; you may ask here our @Robert Israel, possibly others too).
This is only an association due to the form of the required polynomials. The key words are ferromagnetic models, (generalize!) Ising models, Lee-Yang circle theorem, David Ruelle's papers and monographies(!) (the old classic "Rigorous Statistical Mechanics", and a much newer one), Joseph Slawny's papers, etc. (@Robert made significant contributions to Statistical Mechanics, and he should tell us more--my own active contact with this wonderful branch of mathematics was unfortunately short).