Static crossover behavior in the neighborhood of a Lifshitz point

We consider the phase transition from the para- to the ferro- phase for a system in which an m-fold Lifshitz point exists. Nearby the Lifshitz point, the critical behavior at finite distance from Tc is nonasymptotic, described by crossover phenomena, and strongly influenced by the Lifshitz point. The asymptotic behavior on the para-ferro segment of the critical line belongs to the universality class of an isotropic magnet with short-range interaction, with an upper critical dimension dc=4. The crossover depends on the nonuniversal static parameters further away from the critical temperature Tc(x), especially on the dispersion (wave-vector dependence) in the quadratic part of Landau-Ginzburg-Wilson Hamiltonian. The susceptibility and the specific heat have been calculated using the field-theoretical renormalization-group procedure. The effective exponents, which characterize the crossover behavior, have also been discussed.