Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism

English

Mayo, Jack J.[Donostia International Physics Center, E-20018 San Sebastián, Spain > > > ; University of Groningen, 9712 CP Groningen, Netherlands > > > ; Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, Netherlands]

Fan, Zhijie[Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA]

Chern, Gia-Wei[Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA]

Del Campo Echevarria, Adolfo[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]

[en] We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink-number distribution to assess adiabaticity and its breakdown.We consider linear, nonlinear, and exponential cooling schedules, among which the last provides the most efficient shortcuts to cooling in a given quench time. The nonthermal behavior of the final state is established by considering the trace norm distance to a canonical
Gibbs state.