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Numerical simulation of Kibble-Zurek mechanism with Landau-Ginzburg dynamics

Fumika Suzuki

Published Sep 25, 2024• 0 citations
OpenAlex

Abstract

Kibble-Zurek mechanism:non-equilibrium dynamics and defect formulation in systems that cross second-order phase transitions.

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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.
The Kibble-Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant t^\hat tt^ when the order parameter catches up with the post-transition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well we analyze Landau-Ginzburg model and show why temporal evolution of the order parameter plays such a key role. The analytical solutions we obtain suggest novel, hitherto unexplored, experimentally accessible observables that can shed light on symmetry breaking dynamics while testing the conjecture on which the KZM is based.