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We present a symmetry-based method for obtaining suitable tensor descriptionsof lattice vertex functions without spinor components. The approach is based onfinding the polynomial functions of vertex momenta, which satisfy theappropriate tensor transformation laws under hypercubic symmetrytransformations. We use the method to find the most general possible (up tofinite volume effects) basis decompositions for lattice vectors and second-ranktensors. The leading-order non-continuum versions of these representations arethen applied to the Landau gauge gluon propagator and ghost-gluon vertex ofMonte Carlo simulations, to reveal two interesting insights. First, it isdemonstrated numerically and analytically that there exist special kinematicconfigurations where the basis descriptions of both functions reduce to theircontinuum analogues. Second, for the gluon two-point correlator it is shownthat the rate at which the function approaches its continuum form in theinfrared is independent of the lattice gauge coupling $\beta$ (when working inlattice units): the said rate depends on kinematics alone and is ultimatelydictated by the numerical gauge-fixing procedure. We also comment on how thisreflects on the lattice investigations of the anomalous magnetic moment of themuon. Finally, we argue how our findings can be used to directly test some ofthe continuum extrapolation methods.

Tensor representations of lattice vertices from hypercubic symmetry