Continuous symmetry breaking along the Nishimori line

Abstract

We prove continuous symmetry breaking in three dimensions for a special class of disordered models described by the Nishimori line. The spins take values in a group such as ${\mathbb{S}}^1$, $SU(n)$ or $SO(n)$. Our proof is based on a theorem about group synchronization proved by Abbe, Massoulié, Montanari, Sly and Srivastava [AMM+18]. It also relies on a gauge transformation acting jointly on the disorder and the spin configurations due to Nishimori [Nis81, GHLDB85]. The proof does not use reflection positivity. The correlation inequalities of [MMSP78] imply symmetry breaking for the classical $XY$ model without disorder.

22 pages. (Added 1. The case where a (quenched) magnetic field is applied at each vertex 2. Symmetry breaking of left-isoclinic rotations for classical O(4) model and 3. How to recover Long-range-order for classical XY model using [MMSP78])

References in corpus (1)

• Gauge Theory for Quantum Spin Glasses

Cited by in corpus (7)

• Anomalous distribution of magnetization in an Ising spin glass with correlated disorder
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Temperature chaos as a logical consequence of the reentrant transition in spin glasses
• Phase Transitions, Spontaneous Symmetry Breaking, and Goldstone's Theorem
• Dynamical critical behavior on the Nishimori point of frustrated Ising models
• Toward mean-field bound for critical temperature on Nishimori line
• Phase transitions for the $XY$ model in non-uniformly elliptic and Poisson-Voronoi environments