Lee yang theory for cosmological many body problem

We study the phase transition in a gravitating system by analyzing grand canonical partition function as a function of complex fugacity. We extend the Yang-Lee theory to study phase transitions in the gravitational galaxy clustering of galaxies having a variety of masses. This generalizes our previous work based on the same theory for the single-component system to a multicomponent system. We find that galaxy clustering is sensitive to masses and number densities of individual galaxies at early stages while at later stages collective behavior of the particles is more pronounced. This validates our earlier work obtained from different considerations.