  Abstract polymer models are systems of weighted objects, called polymers,
equipped with an incompatibility relation. An important quantity associated
with such models is the partition function, which is the weighted sum over all
sets of compatible polymers. Various approximation problems reduce to
approximating the partition function of a polymer model. Central to the
existence of such approximation algorithms are weight conditions of the
respective polymer model. Such conditions are derived either via complex
analysis or via probabilistic arguments. We follow the latter path and
establish a new condition---the clique dynamics condition---, which is less
restrictive than the ones in the literature. We introduce a new Markov chain
where the clique dynamics condition implies rapid mixing by utilizing cliques
of incompatible polymers that naturally arise from the translation of
algorithmic problems into polymer models. This leads to improved parameter
ranges for several approximation algorithms, such as a factor of at least
$2^{1/\alpha}$ for the hard-core model on bipartite $\alpha$-expanders.
