  Monte Carlo (MC) simulations and series expansion (SE) data for the energy,
specific heat, magnetization and susceptibility of the ferromagnetic 4-state
Potts model on the square lattice are analyzed in a vicinity of the critical
point in order to estimate universal combinations of critical amplitudes. The
quality of the fits is improved using predictions of the renormalization group
(RG) approach and of conformal invariance, and restricting the data within an
appropriate temperature window.
  The RG predictions on the cancelation of the logarithmic corrections in the
universal amplitude ratios are tested. A direct calculation of the effective
ratio of the energy amplitudes using duality relations explicitly demonstrates
this cancelation of logarithms, thus supporting the predictions of RG.
  We emphasize the role of corrections of background terms on the determination
of the amplitudes. The ratios of the critical amplitudes of the
susceptibilities obtained in our analysis differ significantly from those
predicted theoretically and supported by earlier SE and MC analysis. This
disagreement might signal that the two-kink approximation used in the
analytical estimates is not sufficient to describe with fair accuracy the
amplitudes of the 4-state model.
