PurposeSelecting a Monte Carlo (MC) radiation transport code and nuclear physics model affects the simulation of secondary neutron fluence energy spectra and the estimation of the neutron dose equivalent in proton therapy. This study compares the MC codes FLUKA, MCNPX and GEANT4 from previous work with two additional MC codes, TOPAS (with either the Binary Intra-nuclear Cascade (BIC) or the Bertini intra-nuclear cascade model (Bert)) and PHITS (with either the Intra-Nuclear Cascade of Liege (INCL) or the Bert model), to facilitate a more comprehensive comparison. Material and methodsSecondary neutron fluence energy spectra were scored at different locations inside a water phantom, exposed to a 10 × 10 cm2 parallel mono-energetic proton beam with energies of 110 MeV, 150 MeV, 180 MeV and 210 MeV. The neutron dose equivalent was estimated by applying fluence-to-dose equivalent conversion coefficients. ResultsDiscrepancies between MC codes and physics models reach 90 % for the total neutron fluence. Differences are most pronounced in the forward direction of the beam due to a notable presence of high-energy neutrons and the higher uncertainty on the neutron cross-section data for these neutrons. Nuclear model selection within PHITS (INCL or Bert) and TOPAS (BIC or Bert) shows a worse agreement for the Bert model than for the other MC codes and nuclear models. The discrepancies in the neutron spectrum simulations propagate into differences in the estimated neutron dose equivalents. They are more prominent for distal positions (up to a factor of 3) than for lateral positions (up to a factor of 2) and decrease at higher proton energies. ConclusionsThis study shows considerable differences in the out-of-field neutron fluence energy spectra calculated by different MC codes and nuclear physics models. Differences in the neutron dose equivalent reach a factor of 3. The discrepancies are most apparent in distal positions and at lower proton energies.