Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip

TL;DR

This paper extends the Kibble-Zurek mechanism to non-adiabatic initial conditions, proposing a new finite-time scaling framework that accounts for critical initial slip and is validated through numerical simulations.

Contribution

It introduces a unified scaling theory combining finite-time scaling with critical initial slip for non-adiabatic dynamics near critical points.

Findings

Identifies a new length scale from driving that replaces the adiabatic stage.

Proposes a relaxation–finite-time scaling–adiabatic scenario.

Validates the theory with numerical simulations of a 2D Ising model.

Abstract

The Kibble-Zurek mechanism demands an initial adiabatic stage before an impulse stage to have a frozen correlation length that generates topological defects in a cooling phase transition. Here we study such a driven critical dynamics but with an initial condition that is near the critical point and that is far away from equilibrium. In this case, there is no initial adiabatic stage at all and thus adiabaticity is broken. However, we show that there again exists a finite length scale arising from the driving that divides the evolution into three stages. A relaxation--finite-time scaling--adiabatic scenario is then proposed in place of the adiabatic--impulse--adiabatic scenario of the original Kibble-Zurek mechanism. A unified scaling theory, which combines finite-time scaling with critical initial slip, is developed to describe the universal behavior and is confirmed with numerical simulations of a two-dimensional classical Ising model.