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