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The holographic complexity has been studied in a background which includes a critical point. We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves towards the critical point. Two significant results of our analysis are that (i) it takes more time for the complexity in field theory dual to become time dependent as one moves away from the critical point and (ii) near the critical point the complexity starts evolving in time linearly sooner compared to the points away from it.
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