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We developed the functional form of the two-point correlation function underthe approximation of fixed particle number density n(bar). We solved thequasi-linear partial differential equation (PDE) through the method ofcharacteristics to obtain the parametric solution for the canonical ensemble.We attempted many functional forms and concluded that the functional formshould be such that the two-point correlation function should go to zero as thevalue of system temperature increases or the separation between the galaxiesbecomes large. Also, we studied the graphical behavior of the developedtwo-point correlation function for large values of temperature T and spatialseparation r. The behavior of the two-point function was also studied from thetemperature measurement of clusters in the redshift range of 0.023 to 0.546.

A simplistic approach to the study of two-point correlation function in galaxy clusters