短程自旋玻璃的零温涨落
Zero-Temperature Fluctuations in Short-Range Spin Glasses
摘要：
本文研究了零温下d维Edwards-Anderson（EA）Ising自旋玻璃中某些非全等基态对（如果它们存在的话）在有限体积内的能量差。我们证明，这个数量的方差相对于耦合增长至少成比例的体积在任何尺寸大于或等于2。我们的结果的一个重要方面是使用的激发介态。作为潜在应用的一个例子，我们用这个结果来限制二维自旋玻璃基态的可能结构。
英文摘要：
We consider the energy difference restricted to a finite volume for certain pairs of incongruent ground states (if they exist) in the d-dimensional Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the variance of this quantity with respect to the couplings grows at least proportionally to the volume in any dimension greater than or equal to two. An essential aspect of our result is the use of the excitation metastate. As an illustration of potential applications, we use this result to restrict the possible structure of spin glass ground states in two dimensions.
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