  The stellar mass spectrum is an important property of the stellar cluster and
a fundamental quantity to understand our Universe. The fragmentation of diffuse
molecular cloud into stars is subject to physical processes such as gravity,
turbulence, thermal pressure, and magnetic field. The final mass of a star is
believed to be a combined outcome of a virially unstable reservoir and
subsequent accretion. We aim to clarify the roles of different supporting
energies, notably the thermal pressure and the magnetic field, in determining
the stellar mass. Following previous studies by Lee & Hennebelle (2018a,b), we
perform a series of numerical experiments of stellar cluster formation inside
an isolated molecular clump. By changing the effective equation of state (EOS)
of the diffuse gas (that is to say gas whose density is below the critical
density at which dust becomes opaque to its radiation) and the strength of the
magnetic field, we investigate whether any characteristic mass is introduced
into the fragmentation processes. The EOS of the diffuse gas, including the
bulk temperature and the polytropic index, does not affect significantly the
shape of the stellar mass spectrum. The presence of magnetic field slightly
modifies the shape of the mass spectrum only when extreme values are applied.
This study confirms that the peak of the IMF is primarily determined by the
adiabatic high-density end of the EOS that mimics the radiation inside the
high-density gas. Furthermore, the shape of the mass spectrum is mostly
sensitive to the density PDF, and the magnetic field has likely only a
secondary role. In particular, we stress that the Jeans mass at the mean cloud
density and at the critical density are not responsible of setting the peak.
