波茨自旋玻璃中的色彩对称破缺

arXiv - MATH - Probability Pub Date : 2024-09-16 DOI:arxiv-2409.10437

Jean-Christophe Mourrat

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摘要

波茨自旋玻璃是谢林顿-柯克帕特里克（Sherrington-Kirkpatrick）模型的一个类似物，其中每个自旋都可以取$\kappa$可能值中的一个，我们将其解释为颜色。有人在 arXiv:2310.06745 中提出，这个模型的阶次参数在颜色的排列上总是不变的。我们在这里证明，只要 $\kappa \ge 58$，这就是假的。

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Color symmetry breaking in the Potts spin glass

The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in which each spin can take one of $\kappa$ possible values, which we interpret as colors. It was suggested in arXiv:2310.06745 that the order parameter for this model is always invariant with respect to permutations of the colors. We show here that this is false whenever $\kappa \ge 58$.

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arXiv - MATH - Probability

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