Kibble-Zurek Mechanism in the Ginzburg Regime: Numerical Experiment in the Ising Model

TL;DR

This paper numerically tests the Kibble-Zurek mechanism in a two-dimensional Ising model with large thermal fluctuations, confirming initial defect formation predictions but highlighting the importance of defect annihilation dynamics.

Contribution

First numerical verification of the Kibble-Zurek mechanism in a strongly fluctuating, non-mean-field system like the 2D Ising model.

Findings

Initial defect density matches theoretical predictions

Most defects are annihilated before leaving the Ginzburg regime

Final defect density is governed by annihilation dynamics

Abstract

Kibble-Zurek mechanism is a theory of defect formation in a non-equilibrium continuous phase transition. So far the theory has been successfully tested by numerical simulations and condensed matter experiments in a number of systems with small thermal fluctuations. This paper reports first numerical test of the mechanism in a system with large thermal fluctuations and strongly non-mean-field behavior: the two dimensional Ising model. The theory predicts correctly the initial density of defects that survive a quench from the disordered phase. However, before the system leaves the Ginzburg regime of large fluctuations most of these defects are annihilated and the final density is determined by the dynamics of the annihilation process only.