  The axial magnetic effect (AME) is one of the anomalous transport phenomena
in which the energy current is induced by an axial magnetic field. Here we
numerically study the AME for the relativistic Wilson fermion in the axial
magnetic field and a twisted Dirac semimetal. The AME current density inside
the bulk is nonzero, and particularly in the low energy regime for the former
model, it is explained by the field-theoretical results without any fitting
parameter. However, for both models, the average AME current density vanishes
owing to the surface contribution. The axial gauge field is regarded as the
spatially modulated (effective) Zeeman field and induces the spatially
modulated energy magnetization. The AME is attributed to the magnetization
energy current and hence cannot be observed in transport experiments.
