Complexity growth rate during phase transitions

TL;DR

This paper explores how complexity growth rates are affected by phase transitions in various models, revealing links between potential functions, entropy, and dynamical properties during different types of transitions.

Contribution

It establishes a novel connection between phase transitions and discontinuities in complexity growth rates across multiple theoretical models.

Findings

Complexity growth rates exhibit discontinuities at phase transition points.

First order phase transitions show sharp changes in complexity behavior.

Connections between potentials, entropy, and quasinormal modes are identified during transitions.

Abstract

We present evidences 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 the dyonic black holes which are dual to van der Waals fluids, we find a similar first order phase transition in the behavior of complexity growth rate. We then compare the Schwinger effect and also the behavior of complexity in the 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, speed of sounds and complexity growth rates during crossover, first and second order phase transitions and also the behavior of quasinormal modes.