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Color symmetry breaking in the Potts spin glass

Jean-Christophe Mourrat

Abstract

The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in which each spin can take one of $κ$ 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 $κ\ge 58$.

Color symmetry breaking in the Potts spin glass

Abstract

The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in which each spin can take one of 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 .
Paper Structure (2 theorems, 16 equations)

This paper contains 2 theorems, 16 equations.

Key Result

Theorem 1

There exists an explicit functional $\mathscr P_\beta : \bigcup_{d \in \mathscr D} \Pi_d \to \mathbb{R}$ such that for every $d \in \mathscr D$, As a consequence,

Theorems & Definitions (3)

  • Theorem 1: pan.potts
  • Theorem 2: Color symmetry breaking
  • proof