# Many-body chaos near a thermal phase transition

## TL;DR

This study investigates many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures, revealing how chaos indicators like Lyapunov exponents and butterfly velocities behave near a thermal phase transition.

## Contribution

It provides new insights into the temperature dependence of chaos measures in a relativistic field theory across a thermal phase transition, using classical statistical approximation.

## Key findings

- Lyapunov exponent increases linearly with temperature in the quantum critical regime.
- OTOCs spread ballistically with maximal butterfly velocity at the phase transition.
- Lyapunov exponent approaches the non-interacting limit algebraically.

## Abstract

We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.