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arXiv · 2603.01435

Color symmetry in the Potts spin glass at high temperature

Heejune Kim
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Abstract

We show that color symmetry is preserved at high temperatures in the Potts spin glass model with $κ\ge 3$ colors. Our proof employs the second moment method applied to the balanced model with a suitable centering of the Hamiltonian, while incorporating results from the non-disordered Potts model Ellis--Wang (1990), https://doi.org/10.1016/0304-4149(90)90122-9. For $κ= 2$, we exploit the model's gauge symmetry to show that unbalanced configurations occur with exponentially small probability at all temperatures $β\in [0, \infty]$.

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Heejune Kim. 2026-03-02. Color symmetry in the Potts spin glass at high temperature. https://arxiv.org/abs/2603.01435

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