Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.Comment: 10 pages, 4 figures, typos fixed, references adde

Correlations between Abelian Monopoles and center vortices

We study the correlations between center vortices and Abelian monopoles for SU($3$) gauge group. Combining fractional fluxes of monopoles, center vortex fluxes are constructed in the thick center vortex model. Calculating the potentials induced by fractional fluxes constructing the center vortex flux in a thick center vortex-like model and comparing with the potential induced by center vortices, we observe an attraction between fractional fluxes of monopoles constructing the center vortex flux. We conclude that the center vortex flux is stable, as expected. In addition, we show that adding a contribution of the monopole-antimonopole pairs in the potentials induced by center vortices ruins the Casimir scaling at intermediate regime.Comment: 11 pages, 11 figures, Version accepted for publication in Nucl. Phys.