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.
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