Finite-size scaling phenomenon of nuclear liquid--gas phase transition probes

Based on the isospin-dependent quantum molecular dynamics model, finite-size scaling effects on nuclear liquid--gas phase transition probes are investigated by studying the de-excitation processes of six thermal sources of different sizes with the same initial density and similar $N/Z$. Using several probes including the total multiplicity derivative ($dM_{tot}/dT$), second moment parameter ($M_2$), intermediate mass fragment (IMF) multiplicity ($N_{IMF}$), Fisher's power-law exponent ($\tau$), and Ma's nuclear Zipf's law exponent ($\xi$), the relationship between the phase transition temperature and the source size has been established. It is observed that the phase transition temperatures obtained from the IMF multiplicity, Fisher's exponent, and Ma's nuclear Zipf's law exponent have a strong correlation with the source size. Moreover, by employing the finite-size scaling law, the critical temperature $T_c$ and the critical exponent $\nu$ have been obtained for infinite nuclear matter.