  We study the properties of the double-frequency sine--Gordon model in the
vicinity of the Ising quantum phase transition displayed by this model. Using a
mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain
critical and nearly-off-critical correlation functions of various operators. We
discuss applications of the double-sine-Gordon model to one-dimensional
physical systems, like spin chains in a staggered external field and
interacting electrons in a staggered potential.
