Commensurate-incommensurate phase transitions in one-dimensional chains

We consider one-dimensional systems of classical particles whose potential energy has the form: $$W_{\alpha ,\gamma } = \sum {[\alpha V(x_n )} + F(x_n - x_{n - 1} C\gamma )]$$ The limit of the Gibbs state as T→0 is described in terms of invariant measures of two-dimensional mappings which are constructed with the help ofW_{α, γ}. The dependence of these measures on parametersα, γ is investigated.