Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.033150 |
| _version_ | 1827285732372250624 |
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| author | Jack J. Mayo Zhijie Fan Gia-Wei Chern Adolfo del Campo |
| author_facet | Jack J. Mayo Zhijie Fan Gia-Wei Chern Adolfo del Campo |
| author_sort | Jack J. Mayo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:18:40Z |
| format | Article |
| id | doaj.art-a304a9c382594eb3b53b283c4d705bea |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:18:40Z |
| publishDate | 2021-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-a304a9c382594eb3b53b283c4d705bea2024-04-12T17:12:54ZengAmerican Physical SocietyPhysical Review Research2643-15642021-08-013303315010.1103/PhysRevResearch.3.033150Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanismJack J. MayoZhijie FanGia-Wei ChernAdolfo del CampoWe 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.http://doi.org/10.1103/PhysRevResearch.3.033150 |
| spellingShingle | Jack J. Mayo Zhijie Fan Gia-Wei Chern Adolfo del Campo Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism Physical Review Research |
| title | Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism |
| title_full | Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism |
| title_fullStr | Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism |
| title_full_unstemmed | Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism |
| title_short | Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism |
| title_sort | distribution of kinks in an ising ferromagnet after annealing and the generalized kibble zurek mechanism |
| url | http://doi.org/10.1103/PhysRevResearch.3.033150 |
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