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We introduce the "partial-$p$" operation in a massive Euclidean$\lambda\phi^{4}$ scalar field theory describing anisotropic Lifshitz criticalbehavior. We then develop a minimal subtraction a la$Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an applicationwe compute critical exponents diagrammatically using the orthogonalapproximation at least up to two-loop order and show their equivalence withother renormalization techniques. We discuss possible applications of themethod in other field-theoretic contexts.

Massive minimal subtraction scheme and "partial-$p$" in anisotropic Lifshitz space(time)s