  We discuss an integrable model describing one-dimensional electrons
interacting with two-dimensional anharmonic phonons. In the low temperature
limit it is possible to decouple phonons and consider one-dimensional
excitations separately. They have a trivial two-body scattering matrix and obey
fractional statistics. As far as we know the original model presents the first
example of a model with local bare interactions generating purely statistical
interactions between renormalized particles. As a by-product we obtain
non-trivial thermodynamic equations for the interacting system of
two-dimensional phonons.
