On temperature chaos in Ising and XY Spin Glasses

  • Florent Krza̧ka
  • Published 2003

Abstract

– We argue that the chaotic temperature effect predicted in Ising spin glasses should be stronger when one considers continuous (XY, Heisenberg) kind of spins, due to bigger entropic fluctuations. We then discuss the behavior of 3d spin glasses using the Migdal-Kadanoff Renormalization Group for Ising and XY spins, where we show explicitly that the chaotic length scale, the length beyond which equilibrium configurations are completly reshuffled when one changes temperature, could be far smaller for XY than for Ising spins. These results could thus explain why experiments are seeing a stronger rejuvenation effect for continuous spins. One of the most striking features of spin glasses [1] are the phenomena of rejuvenation and memory [2] when temperature hysteresis cycles are performed. When a spin glass approaches equilibrium, it ages and reduces its susceptibility; however, if one lowers the temperature after one such aging at temperature T1, one sees a restart (a rejuvenation) of the susceptibility aging at temperature T2 < T1, while memory of the previous aging can be retrieved when heating back. More impressive is maybe the fact than many such memory cycles can be performed [3]. One of the possible explanation is to consider the temperature chaos effect, that is the possibility that equilibrium spin configurations at temperatures T1 and T2 are uncorrelated, a property that has been predicted to hold in spin glasses many years ago [4, 5]. The presence of memory is then compatible with rejuvenation because of length scale separation: dynamics at T2 < T1 is so slow that it is not fast enough to destroy the previous ordering (see for instance the ghost domains of [6]). In fact most of spin glass dynamics (see [7] for a classical review) could be explained if one assumes that there is a growing coherence length scale during aging, a sensitivity of equilibrium configurations to temperature and separation of length scales at each temperature [8]. Another very important experimental result is the fact that rejuvenation is stronger for Heisenberg than for Ising spins [3,9–11]: the sharpness of these effects appears to decrease continuously with the spin anisotropy. The purpose of this paper is to argue that this might be simply due to a stronger temperature chaos for continuous (XY, Heisenberg) spins, and to provide a simple model to illustrate this assumption. Also, since it has been explained recently “why temperature chaos is hard to

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Cite this paper

@inproceedings{Krzaka2003OnTC, title={On temperature chaos in Ising and XY Spin Glasses}, author={Florent Krza̧ka}, year={2003} }