Dynamical off-equilibrium scaling across magnetic first-order phase transitions

Stefano Scopa, Sascha Wald

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Abstract

We investigate the off-equilibrium dynamics of a classical spin system with symmetry in 2  <  D  <  4 spatial dimensions and in the limit . The system is set up in an ordered equilibrium state and is subsequently driven out of equilibrium by slowly varying the external magnetic field h across the transition line at fixed temperature . We distinguish the cases where the magnetic transition is continuous and where the transition is discontinuous. In the former case, we apply a standard Kibble–Zurek approach to describe the non-equilibrium scaling and formally compute the correlation functions and scaling relations. For the discontinuous transition we develop a scaling theory which builds on the coherence length rather than the correlation length since the latter remains finite for all times. Finally, we derive the off-equilibrium scaling relations for the hysteresis loop area during a round-trip protocol that takes the system across its phase transition and back. Remarkably, our results are valid beyond the large-n limit.
Original languageEnglish
Number of pages27
JournalJ. Stat. Mech.
Volume2018
DOIs
Publication statusPublished - 20 Nov 2018
Externally publishedYes

Bibliographical note

This is the Accepted Manuscript version of an article accepted for publication in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1742-5468/aaeb46

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • cond-mat.stat-mech

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