  Magnetic field effects on free nucleons are studied in peripheral collisions
of $^{197}$Au + $^{197}$Au at energies ranging from 600 to 1500 MeV/nucleon by
utilizing an isospin-dependent quantum molecular dynamics (IQMD) model. With
the help of angular distributions and two-particle angular correlators, the
magnetic field effect at an impact parameter of 11 fm is found to be more
obvious than at an impact parameter of 8 fm. Moreover, the results suggest that
with an increase in the number of peripheral collisions, protons are more
easily condensed with the magnetic field. Magnetic field effects are further
investigated by the ratio of free neutrons to free protons as functions of a
two-particle correlator $C_{2}$, four-particle correlator $C_{4}$ and
six-particle correlator $C_{6}$ of angle $\phi$, rapidity $Y$ and transverse
momentum $p_{T}$. The results show that weak magnetic field effects could be
revealed more clearly by these multiple-particle correlators, with the larger
number of particle correlators demonstrating a clear signal. The results
highlight a new method to search for weak signals using multi-particle
correlators.
