The galaxy-galaxy correlation function as an indicator of critical phenomena in cosmology

We approximate the observable Universe by a collection of equal mass galaxies linked into a many body system by their mutual gravitational interaction. Under the assumptions of (i) nonrelativistic approximation and (ii) global quasi-equilibrium, the partition function of this system can be cast in terms of Ising model spin variables and maps exactly onto a three-dimensional scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the phenomenological/observational value of 1.6 to 1.8.