Complexity growth rate during phase transitions

We present evidence for the connection between the potential of different fields and complexity growth rates both in conformal and confining cases. By studying different models, we also establish a strong connection between phase transitions and the discontinuities in the complexity growth rates. In the first example, for dyonic black holes that are dual to van der Waals fluids, we find a similar first-order phase transition in the behavior of the complexity growth rate. We then compare the Schwinger effect and also the behavior of complexity in the anti-de Sitter (AdS) and AdS soliton backgrounds and comment on the connection between them. Finally, in a general Gubser model of QCD, we present the connections between the potentials, entropies, speeds of sound, and complexity growth rates during crossover and first- and second-order phase transitions, and also the behavior of quasinormal modes.