Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling $z=2$, and show that the renormalization is possible without resort to the renormalization of the coupling constant due to the improvement of UV divergence. Moreover, the IR divergence can be also solved for the massless case of $m^2 =0$, because of the absence of the logarithmic divergence. For a massive case, we obtain a condition for the symmetry breaking. Finally, we investigate whether the critical temperature can exist or not in this approximation. The physical consequences of the other logarithmic divergence free model is discussed.

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