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 $T_c$ 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 $d_c=4\mathrm{}$. The crossover depends on the nonuniversal static parameters further away from the critical temperature $T_c\mathrm{}\left(x\right)\mathrm{}$, 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.