Ensemble Dependent Holographic Phase Transitions in 4$D$ Dyonic AdS Black Holes (2407.11058v6)

Abstract: This work aims to explore the holographic dual of the thermodynamics of 4-D dyonic AdS black holes within the AdS/CFT correspondence framework. With the alterations in $\Lambda$ as cosmological constant and $G_N$ as Newton's constant, the AdS black hole thermodynamics can be extended. This relates to incorporating the $C$ as CFT central charge and $\mu$ as its chemical potential to the standard pairs of $(T, S)$ that is temperature vs. entropy, and $(p,\mathcal{V})$ as field theory pressure vs. volume as a pair in the dual CFT for conjugate thermodynamic variables. We explore the dyonic system which is rich in phase transitions so the traditional pairs for potential and charges become $(\tilde{\Phi}_e,\tilde{Q}_e)$ as electric potential and charge and $(\tilde{\Phi}_m, \tilde{Q}_m)$ as magnetic potential and charge. Exploration of all the 16 ensembles, showed that some show interesting phase behaviour and criticality in some ensembles like $(\tilde{Q}_m,\tilde{\Phi}_e,\mathcal{V},C)$, $(\tilde{Q}_e,\tilde{\Phi}_m,\mathcal{V},C)$, $(\tilde{Q}_m,\tilde{Q}_e,\mathcal{V},C)$ where we get a number of phase transitions and criticality namely Van der Waals, Superfluid $\lambda$ and Davies type where Davies type is missing in the last ensemble. In ensembles $(\tilde{Q}_m,\tilde{\Phi}_e,\mathcal{V},\mu)$, $(\tilde{Q}_e,\tilde{\Phi}_m,\mathcal{V},\mu)$, $(\tilde{Q}_m,\tilde{Q}_e,\mathcal{V},\mu)$, we see only a Davies type phase transitions. In ensemble $(\tilde{Q}_m,\tilde{\Phi}_e,p,C)$, $(\tilde{Q}_m,\tilde{\Phi}_e,p,\mu)$, $(\tilde{Q}_e,\tilde{\Phi}_m,p,C)$, $(\tilde{Q}_e,\tilde{\Phi}_m,p,\mu)$, $(\tilde{\Phi}_m,\tilde{\Phi}_e,p,\mu)$, $(\tilde{Q}_m,\tilde{Q}_e,p,C)$, $(\tilde{Q}_m,\tilde{Q}_e,p,\mu)$ we see no criticality but we do see Davies type phase transition. In ensembles $(\tilde{\Phi}_m,\tilde{\Phi}_e,\mathcal{V},C)$, we see a confined/deconfined and Davies-type phase transition.