This study provides a thorough analysis of the multiplicities of charged particles ( \(\pi ^{\pm }, \varvec{K}^{\pm }\) ) produced in \(p-\varvec{P}b\) collisions at \(\sqrt{s_\textrm{NN}}\) = 5.02 and 8.16 TeV. We utilize the scaled factorial moment (SFM) method to analyze events generated by the AMPT model, specifically examining cases with \(\pi ^0\) and \(\varvec{K}_s^0\) decays both turned off as AMPT (Decay = Off) and both these decays turned on as AMPT (Decay = On). We derive the anomalous fractal dimension ( \(d_q\) ) from the intermittency exponent ( \(\alpha _q\) ) and analyze its variations with changing order \(q\) . Several measures, including the anomalous fractal dimension, degree of multifractality (r), critical exponent ( \(\nu \) ), Lévy index ( \(\mu \) ), and multifractal specific heat (c), show the observed intermittent variations. Additionally, we investigate the quark-hadron phase transition through a second-order phase transition, adopting a scaled factorial moment approach with Ginzburg-Landau theory. This study includes a comparison of critical exponent ( \(\nu \) ) values derived from AMPT-simulated datasets and data from Au+Au collisions at energies ranging from \(\sqrt{s_\textrm{NN}} = \mathbf {7.7}\) to 200 GeV. Also, we have presented a comparison of the generalized fractal dimension ( \(\varvec{D}_q\) ) and specific heat (c) across various emulsion interactions with the AMPT-simulated datasets.
