  We establish the equivalence between the continuum limit of the quantum
spherical model with competing interactions, which is relevant to the
investigation of Lifshitz points, and the O(N) nonlinear sigma model with the
addition of higher order spatial derivative operators, which breaks the Lorentz
symmetry and is known as Lifshitz-type (or anisotropic) nonlinear sigma model.
In the context of the 1/N expansion, we also discuss the renormalization
properties of this nonlinear sigma model and find the nontrivial fixed points
of the beta-functions in various dimensions, which turn out to be connected
with the existence of phase transitions in the quantum spherical model.
