  Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we
develop a general approach to studying mixing times of Glauber dynamics based
on subset expansion expressions for a class of graph polynomials. With a
canonical paths argument, we demonstrate that the chains defined within this
framework mix rapidly upon graphs of bounded tree-width. This extends known
results on rapid mixing for the Tutte polynomial, the adjacency-rank
($R_2$-)polynomial and the interlace polynomial.
