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We study the perturbation of the scalar field interacting with the Maxwellfield in the background of d-dimensional charged AdS black hole and AdSsoliton. Different from the single classical field perturbation, which alwayshas the decay mode in the black hole background, we observe the possiblegrowing mode when the perturbation of the scalar field strongly couples to theMaxwell field. Our results disclose the signature of how the phase transitionhappens when the interaction among classical fields is strong. The suddenchange of the perturbation to growing mode is also observed in the AdS solitonwith electric potential. However in the magnetic charged AdS solitonbackground, we observe the consistent perturbation behavior when theinteraction between scalar field and Maxwell field is considered. This impliesthat for the magnetic charged AdS soliton configuration, unlike the situationwith electric potential, there is no scalar field condensation which causes thephase change.

Signature of the black hole phase transition in quasinormal modes