It is proven rigorously that the ground state in the Edwards–Anderson spin glass model is unique in any dimension for almost all continuous random exchange interactions under a condition that a single spin breaks the global \(\mathbb{Z}_{2}\) symmetry. This theorem implies that replica symmetry breaking does not occur at zero temperature. The site- and bond-overlap are concentrated at their maximal values. Behaviors of short range spin glass models turn out to be much different from those of mean field spin glass models near zero temperature.

中文翻译：

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Edwards–Anderson自旋玻璃模型中基态的唯一性

严格证明，在单个自旋破坏整体的条件下，对于几乎所有连续的随机交换相互作用，Edwards–Anderson自旋玻璃模型的基态在任何维度上都是唯一的 \（\ mathbb {Z} _ {2} \）对称。该定理暗示在零温度下不会发生复制对称性破坏。位点和键的重叠集中在其最大值。事实证明，短程旋转玻璃模型的行为与零温度附近的平均场旋转玻璃模型的行为有很大不同。