Temperature Dependence of Spatial and Dynamic Heterogeneities above the Ising Spin Glass Transition

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ABSTRACT The temperature dependence of the microstructure and local dynamics in the paramagnetic phase of the d -- 2 and d = 3 ±!J Ising spin glass model is examined by comparing the equilibrium distributions of local flip-rates and local energies calculated in large-scale Monte Carlo simulations. The emergence in this model of fast processes as the glass transition is approached corresponds with recent experimental results. INTRODUCTION An open question in the quest to understand the glass transition [1] and the relationship between microstructure, local dynamics, and global relaxation in glass-forming materials, is that of the homogeneity of the material as it is cooled. A number of recent experiments on supercooled liquids and polymers have detected dynamic spatial heterogeneities above the glass transition [2], fueling arguments put forth by numerous groups on the presence of clusters, cooperatively rearranging domains, or coexisting fluids, in such systems [3]. It has been known for some time that the global relaxation in equilibrium glassforming materials above their glass transition temperature is poorly described by a simple exponential, and better described by a stretched exponential at long times. However, it is still not generally known whether individual subdomains relax homogeneously, that is, with each region associated with the same relaxation time and the same stretching exponent, or heterogeneously, that is, with each region having a different relaxation time and/or a different stretching exponent. In systems where the frustration is self-induced, i.e. emerges upon cooling due to packing constraints between the molecules, the relationship between local structure and local dynamics even in computer simulations is difficult to assess due to the time-dependent nature of the local energies and relaxation times. Recently, we have described a detailed computer simulation study of the high temperature, equilibrium phase of a glass-forming system with quenched disorder -- the ±J Ising spin glass -- in both two and three dimensions [4, 5]. This model affords us the opportunity to characterize the temperature dependence of spatial heterogeneities that we know a priori exist in the system due to the quenched disorder. Heterogeneities in such quantities as the local site energy, local flip-rates, local relaxation times, local fields, etc. -- which are absent in the pure Ising ferromagnet -- give rise to complex behavior in the spin glass. For example, we recently reported the emergence of a subset of high-frequency, highenergy excitations that increase in magnitude as temperature T decreases toward the spin glass transition temperature Tsg. This phenomenon is a direct consequence of the frustration, and is similar to results of recent measurements of the magnetic susceptibility of an insulating spin glass in which the approach to the glass transition on cooling could be detected from the behavior of the fastest dynamics in the system [6]. In this proceedings, we focus on the role of frustration an

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