We employ the derivative expansion of the nonperturbative renormalization group to address the phenomenon of anisotropic scale invariance and the associated functional fixed points, also known as Lifshitz points, in systems characterized by a scalar order parameter. We demonstrate the existence of the Lifshitz fixed point featuring a nonclassical value of the anisotropy exponent $\theta <1/2$ and provide estimates for values of a set of critical exponents in the physically most relevant case of the three-dimensional uniaxial Lifshitz point $(d,m)=(3,1)$, $m$ denoting the anisotropy index. We compare our predictions with existing estimates from perturbative expansions around dimensionality $d=4+\frac{1}{2}$ as well as those from the $1/N$ expansion.

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• Continuous phase transition
• Renormalization group
• Statistical field theory
• Critical phenomena