Criticality of global monopole charges in diverse dimensions

In this work, we construct charged AdS black holes with a global monopole charge in diverse dimensions and study the thermodynamics. We find a critical monopole charge below which the solution exhibits Van-der Waals like behaviors. In the context of holography, this could be intepreted using the boundary degrees of freedoms. As an example, we study the phase diagram in the four dimensions analytically. We further analyze the microstructures of the solution using Ruppeiner geometry. We find that repulsive interactions dominates for black holes in a wide range of temperatures. However, around the critical point, attractive interactions is dominant and the Ruppeiner scalar curvature shows universal behaviors: it has a critical exponent $2$ and coefficient $-1/8$ in diverse dimensions. Universality of the results is interpreted from the scaling behavior of free energy near the critical point for Van-der Waals like fluids.