Irreversible and Reversible Behavior of Spin Glasses: Broken Ergodicity
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IRREVERSIBLE AND REVERSIBLE BEHAVIOR OF SPIN GLASSES:
BROKEN ERGODICITY
C. M. SOUKOULIS*, G.S. GREST*, and K. LEVIN** *Corporate Research Science Laboratories, Exxon Research and Engineering Company, Linden, New Jersey 07036; "**The James Franck Institute, The University of Chicago Chicago, Illinois 60637 INTRODUCTION Over the past decade, a great deal of effort has gone into However, because understanding the properties of spin glasses [1,2]. these are rather unique systems which show simultaneously apparent phase transition as well as metastable or glassy behavior, progress has been Though it was initially believed that spin glasses could be slow. treated as if they had a true equilibrium phase transition, we now Recently, it has become recognize that this cannot be the whole story. clear that spin glasses are very complex systems, in which irreversible and time dependent effects play an important role. We now know that one In must go beyond the regime of validity of equilibrium thermodynamics. this paper, we will discuss the mountinq evidence, both experimental and theoretical, for why nonequilibrium approaches are essential in order to understand spin glasses. Early theoretical treatments of spin glasses assumed that a thermodynamic equilibrium phase transition existed [1]. This notion was supported by very low frequency history independent a.c. susceptibility measurements which showed a sharp cusp at a well defined temperature Tc [3]. In addition, strong supporting evidence was provided by Mossbauer experiments which found that the spins were freezing at this same temperature Tc [4]. However, the issue was complicated by the fact that heat [5] and resistivity [6] such as specific other experiments, measurements showed no anomaly at Tc; furthermore, neutron scattering It was also observed that while the a.c. data were inconclusive [7]. susceptibility cusp was quite sharp for very small magnetic fields (Ht• 10 Oe), larger values for the field significantly rounded the cusp and Further measurements added shifted the peak to lower temperatures [3]. It was found that to the existing confusion concerning these systems. below Tc the magnetization of a spin glass was generally history dependent [8,9]. A sample cooled in zero applied magnetic field to T,. Tc before the measuring field H was switched on, gave a different result for the magnetization M, than when the sample was cooled below Tc with The zero field cooled (zfc) magnetization showed a the field H on. cusp, while the field cooled (fc) magnetization did not [8,9]. A series of frequency and time dependent studies [10-17], showed In some, but not all spin that kinetic effects were very important. glasses, the transition temperature Tc increased as the a.c. measuring From this data, it is not possible to frequency increased [13-15]. conclude whether or not a laboratory spin glass has a true thermodynamic What is known is that spin glasses show strong phase transition. irreversible and time dependent effects and that irreversibility apparently sets in at the "t
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