Crossover from string to cluster dynamics following a field quench in spin ice

We investigate quench dynamics of spin ice after removal of a strong magnetic field along the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>[</a:mo><a:mn>100</a:mn><a:mo>]</a:mo></a:mrow></a:math> crystal direction, using Monte Carlo simulations and theoretical arguments. We show how the early time relaxation of the magnetization can be understood in terms of nucleation and growth of strings of flipped spins, in agreement with an effective stochastic model that we introduce and solve analytically. We demonstrate a crossover at longer times to a regime dominated by approximately isotropic clusters, which we characterize in terms of their morphology, and present evidence for a percolation transition as a function of magnetization.