An investigation on the presence of the forwardbackward correlations in the pions multiplicity, emitted in 16 O − Ag/Br interactions at energy E lab = 60 A GeV are carried out. The study of the forward-backward correlation between various observables which is separated by two different pseudorapidity intervals can be treated as an important probe to defining the primordial conditions for the formation of the Quark Gluon Plasma (QGP). We have observed the dependency of correlation fluctuations and correlation strength on pseudorapidity (η) and the increasing width of the pseudorapidity bin size Δη. The roughness of the multiplicities and the particle number deviations are also investigated. The nuclear photographic emulsion technique has been employed to collect the experimental data. We have performed the FRITIOF and Ultra-relativistic Quantum Molecular Dynamics (UrQMD) simulations to compare the experimental results with the simulated results. The analysis strongly indicates the presence of forward-backward correlations in the experimental distributions of pions beyond statistical noise. We have also analyzed the ring-and jet-like structure to confirm the presence of the forward-backward correlations in the multiplicities of 16 O − Ag/Br interactions at 60 A GeV. We have also taken the variations of correlation fluctuations and correlation strength in η and Δη space, respectively for the ring-like and jet-like structure. The average behavior of correlation parameters of ring-like events strongly differs from jet-like events due to expected Cherenkov Gluon radiation.

Visibility graphs (VGs), horizontal visibility graphs (HVGs) and the sandbox algorithm (SB) are applied for multifractal characterization of complex network systems that are converted from time series measurements, are used to characterize the fluctuations in pseudorapidity densities of singly charged particles produced in [Formula: see text]O–AgBr interactions at 60[Formula: see text]A[Formula: see text]GeV. The work presents the analysis of ring-like and jet-like events in terms of multifractality characterization of [Formula: see text]O–AgBr interactions at 60[Formula: see text]A[Formula: see text]GeV. We systematically compared the experimental events of both ring- and jet-like events with Monte Carlo (MC) simulated events. The investigation reveals that the multifractal spectrum for the jet-like events and ring-like events is different and can be distinguished. The ring-like events have its parameters slightly higher than that of jet-like events. Further analysis shows that the strength of the nonstatistical fluctuations is larger for ring-like events than those of jet-like events. The SB method presented here appears to be more useful than the conventional methods used for multifractal characterization.

The two-dimensional intermittency and its self-affine nature are investigated for p–p collisions at [Formula: see text][Formula: see text]TeV in the two-dimensional anisotropic [Formula: see text] space. The UrQMD model has been employed to generate and accumulate the p–p collisions data. Our investigation is made in the framework of scaled factorial moment (SFM) method. The concept of Hurst exponent [Formula: see text] is incorporated to bring a qualitative comparison between the UrQMD generated minimum bias (MB) events and the events at a particular impact parameter [Formula: see text] fm. The variation of the fractal strength with the variation of [Formula: see text] as well as with the variation of the order of the moment [Formula: see text] has been analyzed. Also, the nonlinearity in the variation of SFM with that of [Formula: see text] has been accompanied in this paper. It is observed that the fractal strength and the intermittent type of fluctuations are found to be much stronger in the region with [Formula: see text] compared to the region with [Formula: see text] and the self-affine nature in the fluctuations increases as [Formula: see text] deviates from unity.

In this paper, a detailed study of the multiplicities of charged particles produced in [Formula: see text]–[Formula: see text] collisions, at [Formula: see text][Formula: see text]TeV, has been carried out. Analysis of UrQMD generated events along pseudo–rapidity ([Formula: see text]), azimuthal angle ([Formula: see text]) and [Formula: see text]-[Formula: see text] phase spaces is made with the help of scaled factorial moment method. The results have also been compared with the UrQMD events with finite impact parameter ([Formula: see text]) and minimum bias (MB) conditions. From the intermittency exponent ([Formula: see text]), the anomalous fractal dimension [Formula: see text] is derived and the variations of [Formula: see text] with order [Formula: see text] are investigated. The observed intermittent fluctuations are manifested by various parameters such as anomalous fractal dimension [Formula: see text], degree of multifractality ([Formula: see text]), critical exponent ([Formula: see text]), Levy index ([Formula: see text]) and multifractal specific heat. In the framework of Ginzburg–Landau theory, the second-order phase transition in the light of scaled factorial moment method has also been carried out to search for the quark-hadron phase transition. It is observed that the intermittent type of fluctuations are strong enough in [Formula: see text]-[Formula: see text] space compared to the one-dimensional [Formula: see text] space and [Formula: see text] space. The data reflects the signature of multifractality in [Formula: see text] space and [Formula: see text]-[Formula: see text] space. Whereas in case of [Formula: see text] space, it shows the evidence of monofractality. It is also interesting to note that the values of critical exponents for all impact parameters indicate the apparent existence of quark hadron phase transition except for MB events. However, no such behaviour is observed in [Formula: see text] space. From the knowledge of generalized fractal dimension [Formula: see text], multifractal specific heat is derived from scale factorial moment analysis in case of one-dimensional [Formula: see text] space, [Formula: see text] space and two-dimensional [Formula: see text]-[Formula: see text] space.

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