  The Gibbs measures of an interaction can behave chaotically as the
temperature drops to zero. We observe that for some classical lattice systems
there are interactions exhibiting a related phenomenon of sensitive dependence
of Gibbs measures: An arbitrarily small perturbation of the interaction can
produce significant changes in the low-temperature behavior of its Gibbs
measures. For some one-dimensional XY models we exhibit sensitive dependence of
Gibbs measures for a (nearest-neighbor) interaction given by a smooth function,
and for perturbations that are small in the smooth category. We also exhibit
sensitive dependence of Gibbs measures for an interaction on a classical
lattice system with finite-state space. This interaction decreases
exponentially as a function of the distance between sites; it is given by a
Lipschitz continuous potential in the configuration space. The perturbations
are small in the Lipschitz topology. As a by-product we solve some problems
stated by Chazottes and Hochman.
