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The fractal and phase transitional properties of each type of pions (i. e. ^, 0) through one-dimensional -space, at an energy of s=13~TeV, have been studied with the help of the Scaled Factorial Moment (SFM) framework. To generate simulated data sets for pp collisions under the minimum bias (MB) condition at s=13~TeV, we have employed the Monte Carlo-based event simulator PYTHIA. Various parameters such as the Levy index (), degree of multifractality (r), anomalous fractal dimension (dq), multifractal specific heat (c) and critical exponent () have been calculated. To study the Bose Einstein (BE) effect due to identical particles (here pions) we have also derived these parameters for mixed pion pairs (i. e. \^{+, ^-\}, \^{+, ^0\} and \^{-, ^0\}) and we find that the effects of identical particles weakened for the mixture with respect to the individual distributions. The quest for the quark-hadron phase transition has also been conducted within the framework of the Ginzburg-Landau (GL) theory of second-order phase transition. Analysis revealed that for PYTHIA-generated MB events, there is a clear indication of the quark-hadron phase transition according to the GL theory. Furthermore, the values of the multifractal specific heat (c) for each ^+, ^-, ^0 and the mixture pair data sets of pions generated by PYTHIA model at MB condition, indicate a transition from multifractality to monofractality in pp collisions at s=13~TeV.
Biswas et al. (Sat,) studied this question.